A biopotential sensor, device and process

ABSTRACT

In one embodiment the invention provides a process of capturing a biopotential signal at a surface of a body using a sensor receiver which forms a first signal connection the body wherein one or more parameters of impedance of the first signal connection are unknown. The process comprises receiving the biopotential signal at an output of a first signal channel having a first transfer function which is dependent on the one of more unknown first impedance parameters. The process also comprises receiving the biopotential signal at an output of a second signal channel having a second transfer function dependent on the one of more unknown first impedance parameters. The process also comprises deriving a set of relations for the biopotential signal. The set of relations is defined dependent on the transfer function of the first signal channel, the transfer function of the second signal channel, and outputs of the first and second signal channels; and solving the set of relations to determine the captured biopotential signal.

FIELD OF THE INVENTION

This invention relates to improvements in respect of sensingbiopotential signals, such as sensing biopotential signals at thesurface of a body or, more specifically, sensing biopotential signals atthe skin of a body.

BACKGROUND OF THE INVENTION

In various applications it is desirable to sense and/or measurepotential signals of a body. In some applications the potential signalis a biological potential signal, or biopotential signal. In someapplications a potential signal may be a voltage potential signal. Invarious applications the potential signal may need to be sensed at thesurface of the body. In some applications the body is a human or animalbody.

In various applications it is desirable to sense biopotential signalsnon-invasively. This may involve sensing the biopotential signal at thesurface of a body.

One common application for sensing potential signals at the surface of abody is Electrocardiography. Electrocardiography (ECG or EKG) is theprocess of recording the electrical activity of the heart over a periodof time using electrodes placed at the skin of the body of a subject.These electrodes detect a biopotential signal in the form of smallelectrical changes on the skin that arise from the heart muscle'selectrophysiologic pattern of depolarizing and repolarizing during eachheartbeat.

Conventionally the ECG electrodes are electrically connected to the skinto receive this ECG signal. These conventionally involve a sensorreceiver with an electrode and an adhesive pad which accommodateconductive gel between an electrode and the skin of the subject.

Various problems arise with conventional electrical connection for ECGsignals, or other biopotential signals.

Some of these problems arise from the nature of skin as an organ of abiological body.

Various problems arise in the use of a conductive gel.

Particular problems arise in longevity of the connection to skin forsensing biopotential signals. Particular problems arise in theelectrical properties of conventional sensor receivers.

Some conventional devices are known which sense a biopotential signalusing a capacitive coupling between a body and an electrode.

A problem that arises with some capacitive coupling devices poor signalto noise due to constraints on impedance of the capacitive couplingbetween a sensor and a body.

Another problem that arises with some capacitive coupling devices ismotion-induced artefacts on the captured signal.

Another problem that arises with some capacitive coupling devices isconstraints on the capacitive coupling. For example, some devices mayrely on the coupling being purely capacitive and able to maintain acharge. In many applications the coupling is not purely capacitive. Insome applications there may be a resistive component to the couplingwhich bleeds away any charge on the electrode relied upon by the deviceto measure the signal.

It would therefore be of advantage to have a sensor receiver which couldaddress any or all of the above problems, or at least provide the publicwith an alternative choice.

It would therefore be of advantage to have sensor electronics whichcould address any or all of the above problems, or at least provide thepublic with an alternative choice.

DISCLOSURE OF THE INVENTION

In one aspect the invention provides operable to reconstruct abiopotential signal from a signal received at a surface of a body, theapparatus comprising:

a sensor device which forms a first signal connection for thebiopotential signal, the first signal connection having a first sensorimpedance, and which forms a second signal connection for thebiopotential signal, the second signal connection having a second sensorimpedance, wherein the sensor device is arranged such that the secondsensor impedance is linearly related to the first sensor impedance by animpedance relation;sensor circuitry which provides i) a first sensor signal related to thebiopotential signal by a first channel expression which is dependent onparameter values for the sensing circuitry providing the first sensorsignal, dependent on the first sensor impedance and dependent on thebiopotential signal, and ii) a second sensor signal related to thebiopotential signal by a second channel expression which is dependent onparameter values for the sensing circuitry, dependent on the secondsensor impedance dependent on the biopotential signal;a processor operable to read data carrying information on parametervalues of the receiver circuitry, operable to read data carryinginformation on the first sensor signal, operable to read data carryinginformation on the second sensor signal and operable to generate datacarrying information on a reconstruction of the biopotential signal saidgeneration using a derived relation which is derived from a set ofrelations comprising the first channel expression, the second channelexpression and the impedance relation, wherein the biopotential relationis independent of the first sensor impedance.

A channel expression may define a transfer function for a channel.

The signal connection may be represented in a channel expression as oneor more unknown impedance parameters which are eliminated in the derivedexpression used by the processor. The signal connection may have two ormore impedance parameters which are unknown, such as due to propertiesof skin of the body or spacing between the body and a sensor and/orproperties of materials between a sensor and the body and/or propertiesof a sensor device. For example, a signal connection may be intended tobe capacitive only but may have an ohmic parameter which dissipatescharge on an electrode of a sensor. The signal connection may have twoor more impedance parameters which are variable and unknown at any giventime, such as may occur due to motion of the body and/or to a sensorrelative to the body or due to effects occurring at the body.

The receiver circuitry may have components selected so the circuitryprovides the transfer function defined and/or can be described by thechannel expression.

The transfer function of the first channel may comprise an analyticexpression for the gain of a first channel comprising at least one of arelation to the current entering the first channel and a relation to thevoltage signal at the entry of the first channel.

The transfer function of the second channel may comprise an analyticexpression for the gain of a second channel comprising at least one ofan expression to the current entering the second channel and a relationto the signal at the entry of the second channel.

The sensor circuitry may provide a first channel and the first channelexpression is:

V₁ = i_(u1)TF_(1i) + V_(in)TF_(1v) + i_(u1)Z_(u1)TF_(1v)

where i_(u1) is the current entering the channel, V_(in) is the signalat the entry of the channel, V₁ is the output of the first signalchannel, Z_(u1) is the unknown first impedance, TF_(1i) is the relationfor the gain relation to the current entering the channel, TF_(1v) isthe relation for the gain relation to the signal at the entry of thechannel.

The sensor circuitry may provide a second channel and the second channelexpression is:

V₂ = i_(u2)TF_(in) + V_(in)TF_(u 2) + i_(u2)Z_(u2)TF_(2v)

where i_(u2) is the current entering the channel, V_(in) is the signalat the entry of the channel, V₂ is the output of the second signalchannel, Z_(u2) is the unknown second impedance, TF_(2i) is the relationfor the gain relation to the current entering the channel, TF_(2v) isthe relation for the gain relation to the signal at the entry of thechannel.

The first signal channel may comprise the first signal connection inseries with sensor circuitry arranged so that the first channel transferfunction is non-linearly related to the first sensor impedance.

The impedance relation may be:

Z_(u 2) = H₁₂Z_(u 1) + k₁₂

where Z_(u2) is the second sensor impedance Z_(u2) is the first sensorimpedance, H₁₂ is a factor and k₁₂ is a constant.

The derived expression used by the processor:

$V_{in} = {\frac{\begin{matrix}{{H_{12}{i_{u\; 2}( {{- V_{1}} + {i_{u\; 1}{TF}_{1i}}} )}{TF}_{2v}} +} \\{i_{u\; 1}{{TF}_{1v}( {V_{2} - {i_{u\; 2}{TF}_{2i}} + {i_{u\; 2}k_{12}{TF}_{2v}}} )}}\end{matrix}}{( {i_{u\; 1} - {H_{12}i_{u2}}} ){TF}_{1v}{TF}_{2v}}.}$

The processor may be operable to generate data carrying information onan estimate of the unknown first impedance using the relation:

${Z_{u\; 1} = \frac{\begin{matrix}{{( {{- V_{1}} + {i_{\;{u\; 1}}{TF}_{1i}}} ){TF}_{2v}} +} \\{{TF}_{1v}( {V_{2} - {i_{u\; 2}{TF}_{2i}} + {i_{u\; 2}k_{12}{TF}_{2v}}} )}\end{matrix}}{( {i_{u\; 1} - {H_{12}i_{u2}}} ){TF}_{1v}{TF}_{2v}}},$

wherein i_(u1) is a current entering the first channel and i_(u2)entering the second channel.

The receiver circuitry may be operable to output a first currentmeasurement i_(u1) of a current entering the first channel and a secondcurrent measurement i_(u2) entering the second channel.

The circuitry may be arranged so that current entering a signal channelmay be related to the output of the signal channel.

The first channel expression may be a transfer function of a firstchannel and the second channel expression may be a transfer function ofa second channel.

The first channel transfer function may comprise an analytic relationfor the gain of a first channel comprising an operational amplifiercircuit having a selected feedback impedance a selected series impedanceconnected at an input of an operational amplifier and comprising animpedance connected to the selected series impedance to represent thefirst sensor impedance.

The second channel transfer function of the second channel may comprisean analytic relation for the gain of a second channel comprising anoperational amplifier circuit having a selected feedback impedance aselected series impedance connected at an input of an operationalamplifier and comprising an impedance connected to the selected seriesimpedance to represent the second sensor impedance.

The transfer function of the first channel may comprise:

$V_{1} = {{- \frac{Z_{f1}}{Z_{s\; 1} + Z_{u1}}}V_{in}}$

where Z_(f1) is a selected first channel feedback impedance Z_(s1) is aselected first channel series impedance, and the transfer function ofthe second channel comprises

$V_{2} = {{- \frac{Z_{f2}}{Z_{s\; 2} + {H_{12}Z_{u\; 1}} + k_{12}}}V_{in}}$

where Z_(f2) is a selected second channel feedback impedance Z_(s2) is aselected second channel series impedance, and where the capturedbiopotential signal is determined from

${V_{in} = {- \frac{V_{1}{V_{2}( {k_{12} - {H_{12}Z_{s1}} + Z_{s\; 2}} )}}{{{- H_{12}}V_{2}Z_{f1}} + {V_{1}Z_{f2}}}}}.$

The receiver circuitry may comprise a first receiver circuit having atransfer function defined by a first feedback impedance and a firstseries impedance.

The first receiver circuit may be a charge amplifier.

The charge amplifier may be an inverting amplifier with a feedbackimpedance between an output and an inverting input and a seriesimpedance at the inverting input.

The biopotential signal, outputs of the receiver circuitry and sensorimpedances may be defined in the frequency domain and the processor mayoperate in the frequency domain.

The signals and parameters V_(in), V₁, V₂, H₁₂, k₁₂, Z_(s1), Z_(s2),Z_(f1) and Z_(f2) may be in the frequency domain.

The first channel expression may comprise:

$V_{1} = {( {1 + \frac{Z_{f1}}{Z_{1}}} )V_{in}}$

where Z₁ is the first sensor impedance and wherein the second channelexpression comprises

$V_{2} = {( {1 + \frac{Z_{f2}}{Z_{2}}} )V_{in}}$

where Z₂ is the second sensor impedance where the data carryinginformation on the reconstructed biopotential signal is generated by theprocessor using:

${V_{in} = \frac{V_{2}Z_{2}}{Z_{2} + Z_{f2}}}.$

The first channel expression may comprise:

$V_{1} = {( {1 + \frac{Z_{f1}}{Z_{1}}} )V_{in}}$

where Z₁ the first signal impedance signal connection and the transferfunction of the second channel comprises

$V_{2} = {( {1 + \frac{Z_{f2}}{Z_{2}}} )V_{in}}$

where Z₂ is the second impedance signal and where the derived expressionis

$V_{in} = \frac{{i_{u\; 1}V_{2}{Z_{2}( {Z_{1} + Z_{f\; 1}} )}} - {H_{12}i_{u\; 2}V_{1}{Z_{1}( {Z_{2} + Z_{f\; 2}} )}}}{( {i_{u\; 1} - {H_{12}i_{u\; 2}}} )( {Z_{1} + Z_{f\; 1}} )( {Z_{2} + Z_{f\; 2}} )}$

where i_(u1) is the current entering the first input channel and i_(u2)is the current entering the second input channel.

The first channel expression may comprise:

$V_{1} = {\frac{Z_{41}}{Z_{21} + Z_{41}}\frac{( {Z_{11} + Z_{31}} )}{Z_{11}}V_{in}}$

where Z₁₁, Z₂₁, Z₃₁ and Z₄₁ are impedance parameters of the first signalchannel, and the second channel expression may comprise

$V_{2} = {\frac{Z_{42}}{Z_{22} + Z_{42}}\frac{( {Z_{12} + Z_{32}} )}{Z_{12}}V_{in}}$

where Z₁₂, Z₂₂, Z₃₂ and Z₄₂ are impedance parameters of the first signalchannel, and where the captured biopotential signal may be determinedfrom

$V_{in} = {\frac{V_{1}V_{2}Z_{11}{Z_{12}( {Z_{22} - {H_{12}( {Z_{21} + Z_{41}} )} + Z_{42}} )}}{\begin{matrix}{{{- H_{12}}V_{2}{Z_{12}( {Z_{11} + Z_{31}} )}Z_{41}} +} \\{V_{1}{Z_{11}( {Z_{12} + Z_{32}} )}Z_{42}}\end{matrix}}.}$

The transfer function of each of a multiplicity of n signal channels maycomprise:

V_(in) = i_(un)TF_(ni) + V_(in)TF_(nv) + i_(un)Z_(un)TF_(nv)

and the relation between the unknown first impedance parameter andunknown second impedance parameter may comprise

Z_(un) = H_(1n)Z_(u1)

and the captured biopotential signal may determined by the processorusing

$\begin{pmatrix}V_{in} \\Z_{u\; 1}\end{pmatrix} = {\begin{pmatrix}{TF}_{1v} & {{- i_{u\; 1}}{TF}_{1v}} \\{TF}_{2v} & {{- H_{12}}i_{u\; 2}{TF}_{2v}} \\\vdots & \vdots \\{TF}_{nv} & {{- H_{1n}}i_{un}{TF}_{nv}}\end{pmatrix}^{+}\begin{pmatrix}{V_{1} - {i_{u\; 1}{TF}_{1i}}} \\{V_{2} - {i_{u\; 2}{TF}_{2i}} + {i_{u\; 2}k_{12}{TF}_{2v}}} \\\vdots \\{V_{n} - {i_{u\; n}{TF}_{2i}} + {i_{un}k_{1n}{TF}_{nv}}}\end{pmatrix}}$

where A⁺ represents an operator such that if Ax=b, x=A⁺b where Z_(u2) isthe second sensor impedance Z_(u2) is the first sensor impedance, H₁₂ isa factor and k₁₂ is a constant, and where TF_(nv) a transfer function.

An another aspect the invention provides a process of capturing abiopotential signal at a surface of a body using a sensor receiver whichforms a first signal connection with the body wherein one or moreparameters of impedance of the first signal connection are unknown, theprocess comprising:

receiving the biopotential signal at an output of a first signal channelhaving a first channel transfer function which is dependent on the oneor more unknown first impedance parameters;receiving the biopotential signal at an output of one or more secondsignal channels each having a second channel transfer function dependenton the one or more unknown first impedance parameters;solving a set of relations to determine the captured biopotential signalwherein the set of relations is defined dependent on:i) the first channel transfer function,ii) the second channel transfer function, andiv) outputs of the first and second signal channels.

The second channel transfer function may be dependent on the firstunknown impedance parameter by being dependent on a second impedanceparameter which has a known relation to the unknown first impedanceparameter.

The unknown one or more parameters of impedance of the first signalconnection may be the impedance of the first signal connection, and theunknown one or more parameters of impedance of the first signalconnection may be the impedance of the first signal connection,

and the set of relations may be solved to eliminate the first and secondunknown impedance parameters to allow the biopotential signal to bedetermined independently of the impedance of the first or second signalconnections.

The known relation of the unknown second impedance parameter to theunknown first impedance parameter may be an approximation.

The solved set of relations may comprise a first relation which relatesthe biopotential signal to an expression which is dependent on theoutput signal of the first signal channel, the unknown first impedanceparameter and one or more known parameters for components included inthe first signal channel.

The solved set of relations may comprise a second relation which relatesthe biopotential signal to an expression which is dependent on theoutput signal of the second signal channel, an unknown second impedanceparameter and one or more known parameters for components included inthe second signal channel.

The unknown second impedance and one or more known parameters forcomponents included in the second signal channel may be selected suchthat the second relation does not reduce to the first relation.

The derived set of equations comprises a third relation which relatesthe unknown second impedance parameter to unknown first impedanceparameter.

The first signal channel may be arranged to have a transfer functionwhich is non-linear with respect to the unknown first impedanceparameter.

The second signal channel may be arranged to have a transfer functionwhich is non-linear with respect to the unknown first impedanceparameter.

In another aspect the invention provides a process for reconstructing abiopotential signal from first and second sensing signals output bysensing circuitry which receives first and second electrode signals fromfirst and second sensor electrodes which each form a connection for thebiopotential signal, wherein the second sensor electrode is adapted toprovide a signal connection with an impedance which differs from thesignal connection of the first electrode by a linear relationship, theprocess comprising the steps of:

reading first and second sensor signals;reading data carrying information which defines an expression for thebiopotential signal, the expression derived fromi) a first channel expression for the first sensor signal dependent onparameter values for the sensing circuitry providing the first sensorsignal, dependent on the impedance formed by the first electrode anddependent on the biopotential signal, andii) a second channel expression for the second sensor signal dependenton parameter values for the sensing circuitry providing the secondsensor signal, dependent on the impedance formed by the second electrodeand dependent on the biopotential signal, andiii) an expression for the impedance formed by the second electrodedependent on the impedance formed by the first electrode,wherein said expression for the biopotential signal is derived toeliminate the impedance formed by the first electrode and eliminate theimpedance formed by the second electrode; anddetermining the bio-potential signal using said expression for thebiopotential signal to reconstruct the biopotential signal independentlyof the first and second impedance.

In another aspect the invention provides a sensing device for sensingbiopotential signals in a sensing region at a surface of a body, thesensing device comprising:

first and second input terminals for connection to first and secondsensor receivers which each connect the biopotential received at thesurface of the body to a respective receiver terminal, wherein a secondsensor receiver has a second receiver impedance for the biopotentialsignal which has a defined relationship with a first receiver impedanceof the first receiver;sensing circuitry operable to connect to first and second receivers toreceive first and second receiver signals and to apply a definedtransfer function to the first and second receiver signals to outputfirst and second sensing signals; anda sensing processor operable to determine the biopotential signaldependent on the first and second sensing signals, dependent onparameters of the defined transfer function and dependent on the definedrelationship of the first and second receiver impedances.

The defined relationship between the first and second receiverimpedances may be substantially linear.

The sensor receiver may comprise one or more electrodes operable toprovide a capacitive connection for the biopotential signal at thesurface of the body.

The sensor receiver may comprise one or more electrodes operable toprovide a conductive connection for the biopotential signal at thesurface of the body.

The first and second sensor receivers may comprise respective first andsecond electrodes each providing a connection for the biopotentialsignal.

The first and second sensor receivers may have an electrode common toboth receivers.

In another aspect of the present invention provides a sensor operable toreceive a potential signal in a sensing region at a surface of a bodythe sensor receiver having a first electrode and a second electrode toform first and second sensing connections in the sensing region toreceive the potential signal wherein the electrodes are arranged suchthat the second connection has an impedance which approximately relatesan impedance of the first connection by a defined expression.

The defined expression may be a factor.

In another aspect the invention provides a sensor operable to receive apotential signal in a sensing region at a surface of a body the sensorreceiver operable to receive the biopotential signal in the sensingregion, wherein the sensor comprises first and second signal pathways tofirst and second receiver terminals to provide the biopotential signalreceived to sensing electronics wherein second connection has animpedance which approximately relates an impedance of the firstconnection by a defined relation.

In another aspect the invention provides a sensor circuitry for apotential signal received by a sensor electrode over an unknown and/orvariable impedance, the sensor circuitry comprising first and secondoutput channels for first and second output signals each signalcomprising an amplification of the potential signal wherein theamplification is defined by the gain of an operational amplifier with afeedback impedance and with an input impedance wherein the inputimpedance is comprised of said unknown and/or variable impedance and aseries impedance between the sensor electrode and the operationalamplifier.

In another aspect the invention provides a process for reconstructing abiopotential signal from a first and second sensing signals output bysensing circuitry which receives first and second electrode signals fromfirst and second sensor electrodes which each form a connection for thebiopotential signal, the process comprising the steps of:

reading first and second sensor signals;reading data carrying information on a relationship between a firstsensor impedance formed by the first electrode and a second sensorimpedance formed by the electrode;reading data carrying information on expressions for the biopotentialsignal independent of the first and second impedance;determining the bio-potential signals dependent on the first and secondsensor signals, on parameter values for the sensing circuitry anddependent on the relationship between the second sensor impedance andfirst sensor impedance.

BRIEF DESCRIPTION OF THE DRAWINGS

Additional and further aspects of the present invention will be apparentto the reader from the following description of embodiments, given in byway of example only, with reference to the accompanying drawings inwhich:

FIG. 1 illustrates a sensing device for biopotential signal according toan embodiment of the invention;

FIG. 2 further illustrates the sensing device of FIG. 1, showing adielectric layer over the electrode;

FIG. 3 illustrates a biopotential signal which various embodiments ofthe invention are adapted to sense;

FIG. 4 illustrates the effect of an air gap between an electrode of thesensing device of FIG. 1;

FIG. 5 illustrates circuitry representing a biopotential signal, sensorelement and sensing circuitry of the embodiment of FIG. 1 and FIG. 2;

FIG. 6 illustrates circuitry representing a biopotential signal, sensorreceiver and sensing circuitry of an alternative embodiment of FIG. 5;

FIG. 7 illustrates biopotential signals to be sensed and after sensingby sensor and sensing circuitry of the embodiments of FIG. 5 and FIG. 6;

FIG. 8 illustrates a sensor according to further embodiment of theinvention;

FIG. 9 illustrates a biopotential signal element, sensing circuitry andsensing processor according to embodiment of the invention of FIG. 8;

FIG. 10 illustrates circuitry representing a biopotential signal, sensorreceiver and sensor circuitry of a further embodiment of the inventionsimilar to that of FIG. 8 and FIG. 9 with specific implementation ofsensor receiver and sense of circuitry;

FIG. 11 illustrates a process performed by a sensing processor of theembodiment of FIGS. 8 and 9 or the embodiment of FIG. 10;

FIG. 12 illustrates circuitry representing a biopotential signal, sensorreceiver and generalised sensing circuitry according to variousadditional embodiments of the invention;

FIG. 13 illustrates a further embodiment of the present invention; and

FIG. 14 illustrates another embodiment of the present invention.

Further aspects of the invention will become apparent from the followingdescription of the invention which is given by way of example only ofparticular embodiments.

BEST MODES FOR CARRYING OUT THE INVENTION

FIGS. 1 and 2 illustrate an embodiment of the invention adapted toreceive and capture a biopotential signal 1 at a surface 2 of the body3. The biopotential signal Vs is represented by an ideal voltage source4.

As illustrated a sensor receiver, or sensor, 5 is located against thesurface 2 to receive the biopotential signal 1.

In the scenario illustrated in FIGS. 1 and 2, the sensor receiver 5 isplaced against the surface 2. In this example the sensor 5 hasdielectric material 7 arranged on the side of an electrode 8 which facesthe surface 2 so the dielectric material is arranged between the surface2 and the electrode 8 and acts as a dielectric.

In this example, the biopotential signal is received over a capacitiveconnection formed by the surface 2 and electrode 8 which are separatedby dielectric layer 7. The dielectric layer acts as a capacitordielectric. The sensing receiver 5 is connected at a terminal (notshown) to sensing electronics 9. The capacitive connection may bereferred to as a signal connection. Impedance parameters of thecapacitive connection may be referred to as impedance of the sensor 5,or sensor impedance.

Not shown in FIGS. 1 and 2 are locating means such as adhesive materialwhich locates the sensor 5 at the surface of the body. In this examplethe body is a biological body and the surface 2 is skin. In thisembodiment an adhesive is used to affix the sensor 5 to the skin.

In the example illustrated in FIGS. 1 and 2 the electrode is connectedby a terminal 11 to sensing circuitry 9. FIGS. 1 and 2 also illustratethe sensing circuitry 9 connected to a sensing processor 10.

In overview the operation of the sensing device 1 involves the sensor 5being located at the surface 2 of the body 3 to receive a biopotentialsignal 4. Sensing circuitry 9 is connected to the sensor 5 and to asignal for a sensing processor 10. The sensing processor determines thebiopotential signal from a sensing signal received from the sensingcircuitry 9 and dependent on parameter values defining the connectionprovided by sensor 5 and on parameter values defining operation of thesensing circuitry 9.

An air gap 11 may exist between the sensor 5 and the surface 2. Thereader will appreciate that an air gap will represent a low permittivitydielectric for a capacitor formed by the surface 2 and electrode 8. Thecapacitance will therefore vary with the magnitude of the air gap 11.

An illustration of how the air gap, or distance, between the surface 2and sensor electrode 8 is given by considering the capacitance C of twoopposing electrodes with overlapping area A, separated by distance dover a medium with an effective permittivity ϵ is given by:

$\begin{matrix}{C = {ɛ\frac{A}{d}}} & {{Equation}\mspace{14mu} 1}\end{matrix}$

where ε=ε₀ε_(r), ε₀ is the permittivity of vacuum (8.854 pF/m) and ε_(r)is the relative permittivity of the medium between surface 2 and sensorelectrode 8 (in this case, air)

Variations in the capacitance of the capacitive connection provided bythe sensor 5 will result in variations in the impedance of theconnection provided to receive the biopotential signal.

Variations in the impedance of the connection provided by a sensor 5 maybe manifest as variations or artefacts on a signal sensed by the device1.

Variations of the airgap 11 may impact on the capacitive connectionprovided by the sensor 5. In the case of a real body 3 of a biologicalsubject the magnitude of this air gap 11 will vary.

Variations in the air gap 11, or it's effect, may be over the sensingregion 6. Variations in the air gap 11 may be periodic over a timeinterval in which the biopotential signal 1 is to be sensed, or sampled,and within a frequency range of the biopotential signal. This variationmay be an artefact of events in the body. Variation of the air gap 11may be over an extended time in which sensing may be conducted or inwhich different sensing samples might be taken. Variations in the airgapmay be over time with frequency components outside a frequency range ofthe bio potential signal, such as a variation which may be caused by theloosening of adhesive, for example, used to locate the sensor 5 on thesurface. This variation may be as a DC drift in capacitance and/or inthe biopotential signal as sensed by the device 1. Other variations maybe at frequencies above the frequency range of a biopotential signalsuch as might be caused by high frequency vibration. Variations in theair gap may be any combination of the variations discussed above.

In similar scenarios to that illustrated in FIGS. 1 and 2, other effectsmay impact on the impedance of the connection provided by the sensorreceiver. For example, effects at the skin of a subject may affect thepermittivity of the dielectric properties of the capacitor formed by thesurface 2 and electrode 8.

An example effect of variations in the capacitance on a biopotentialsignal are illustrated in FIG. 3. In this example the biopotentialsignal is an Electrocardiography signal (ECG).

The upper trace 51, as shown, illustrates an example simulated ECGsignal. The lower trace 52 illustrates the ECG signal Vecg (equivalentto Vs of FIGS. 1 and 2) sensed as a displacement current id after theeffect of a capacitance C.

$\begin{matrix}{i_{d} = {C\frac{{dV}_{ecg}}{dt}}} & {{Equation}\mspace{11mu} 2}\end{matrix}$

The reader may recognise the effect of the capacitance C is todifferentiate Vecg.

As described above, air acts as a dielectric for a capacitor formed bythe surface 2 and sensor 3 with a low dielectric constant ε_(r)=1. Asthe air gap of the sensor from the surface increases, the air gapcapacitance C_(air) decreases and the low frequency ECG signal getsdifferentiated and attenuated.

The applicant has observed that mitigating the effect of an air gap willallow sensing of an ECG, for example, more robust over variations in anair gap between the surface and the sensor receiver. This may allowsensing of ECGs from a distance away from the surface 2 of the body 3 ofa subject or may allow variations caused by phenomena occurring at abody to be mitigated.

FIG. 4 shows a plot 53 with traces 54 to 67 for different air gapsillustrating the effect of air gap on an ECG signal of voltage 1V sensedcapacitively by another embodiment of the invention, where d representsthe change in distance (in mm). A very slight change in ECG amplitudesis observed at air gaps=0.2 mm with trace 54. The designed sensor iscapable of sensing ECG signals in real conditions from a distance of upto 20 mm, without the incorporation of circuit improvisation techniquessuch as guarding and shielding.

Configurations of various embodiments of the invention which furthermitigate of the effect the ‘air gap effect’ are discussed below.

FIG. 5 illustrates circuitry representing a sensor (not shown) andsensing circuitry 109 according to another embodiment of the invention.In this illustration the capacitance Ce represents an unknowncapacitance of a signal connection a series capacitance 113 connectedbetween the ideal voltage source 104 and the inverting input 114 of anoperational amplifier 115. This capacitance 113 is made up of thecapacitance between the body (not shown, but similar to 3 in FIG. 1) anda sensing electrode (not shown but similar to 8 in FIG. 1) and also by aseries capacitance connected at the input 114 of the Op-Amp 115 as aseries capacitance of a charge amplifier circuit 116. In practicespecific implementations of this embodiment may have series capacitancesconnected to the sensor receiver (not shown) to set the capacitance Ce113 at an optimal value. However, this may be problematic because thecapacitance formed by the body (not shown) and the sensor receiver (notshown) is not known, is not precisely known or varies with effectsoccurring at the body or skin of the body or because of a combination ofthese. Similarly, and impedance associated with the capacitance will beunknown.

The charge amplifier circuit 116 is formed of an operational amplifier115 with supply voltages, feedback components 117 and series componentsforming part of the capacitance 113. As the reader will appreciate thefeedback and series components provide feedback and series impedanceswith known parameter or component values which determine a transferfunction for the charge amplifier according to Kirchhoff's laws appliedat the node 114 of the Op-Amp with assumptions for the operationalamplifier well known to the reader. In this specific example thefeedback impedance is provided by a feedback resistance Rf 119 and afeedback capacitance C_(f) 118, in parallel. The gain of the chargeamplifier 115 will be determined by the feedback impedance and theseries capacitance 113, which includes both the sensor capacitance andany series capacitance included in the charge amplifier circuit 116.

The reader may recognise the sensor connected to the circuit 116 as asignal channel where the circuit has a transfer function defined byknown components and where the transfer function of the channel isdependent on the known component values and also on an unknown impedanceparameter of the signal connection provided by the sensor. For example,the capacitance of the signal connection may vary by an unknown valuemay vary over an unknown range of values.

The sensor circuitry of the embodiment of FIG. 5 provides gaindetermined, or selected, dependent on an expected noise floor for thebiopotential signal. In this example the expected noise floor isdetermined by background electromagnetic emissions.

The components of the embodiment illustrated in FIG. 5 are alsodetermined, on the following considerations. One consideration is thatthe corner frequencies of the charge amplifier are outside a range offrequencies of the biopotential signal. Another consideration is thatthe lower corner frequency eliminates DC drift which may occur due toeffects of the body (not shown), occurring at the surface of the body ata sensing region (not shown) defined by the sensor (not shown). In theexample shown the lower corner frequency is determined to mitigate theeffects of the air gap which occurs between the body (not shown) and thesensor (not shown). In the example shown the lower corner frequency isdetermined to mitigate artefacts of breathing of the subject whichaffect the air gap between the body (not shown) and the sensor (notshown).

Table 1, below, lists values for the capacitance Ce 113, providing aseries impedance, of charge amplifier and noise levels of biopotentialsignals captured via a resistive connection to the body (not shown) anda capacitive connection to the body (not shown).

TABLE 1 Values of series capacitance of charge amplifier used for sensorcircuitry. Noise level Noise level (peak to peak) (peak to peak) Valueof series for resistive for capacitive capacitance (pF) sensing sensing22 0.056 0.05 470 0.9 0.8 2200 2.5 1.8

FIG. 6 illustrates a charge amplifier with a resistive sensor accordingto an alternative embodiment of the invention to FIG. 5. In this examplethe resistive sensing arrangement according to various embodimentsinvolves a direct conductive connection to a surface of a body and thisconnection is characterised by a resistance 153.

An Op-Amp, LMP7721MA, is used in the sensing circuitry 109 of theembodiment illustrated with reference to FIG. 5. The selection of thisOp-Amp is due to ultra-low input bias current characteristics of theLMP7721MA.

FIG. 7 shows plots 160 illustrating the effect on noise of the variouscapacitance values listed in Table 1 with traces 161 of biopotentialsignals sensed with capacitive sensing arrangement of embodiments of theinvention illustrated with reference to FIGS. 1 and 2 traces 162 fortraces of biopotential signals sensed with a conductive sensingarrangement of alternative embodiments.

Table 2 lists component values used for a charge amplifier of theembodiments of the invention illustrated with reference to FIG. 5 andFIG. 6.

TABLE 2 Values of components for sensing circuitry. Passive CircuitComponent Desired Value/range Rf 10 G ohm Cf 10 to 100 pF Cs 22 to 500pF Rs 100 Meg to 1 G

The charge amplifier circuitry of FIGS. 5 and 6 with component valueslisted in Table 2 are selected to be within the following regimecorresponding to the principles discussed above.

The charge amplifier 116 restores the ECG wave shape of a signalreceived at a sensor at a surface of a body by integrating the signaldifferentiated due to air gap or series capacitance between the surfaceof the body and the electrode of the sensor.

Integration is only possible if

$\begin{matrix}{( {R_{f} \times C_{f}} ) > ( {R_{s} \times C_{f}} )} & {{Equation}\mspace{14mu} 3}\end{matrix}$

where R_(f) and C_(f) are the feedback values of resistance andcapacitance and is R_(s) the series resistance.

A series capacitor forming part of 113 Cs and the charge amplifiercircuit 116 provides differentiation of the signals prior to theirintegration, wherein the corner frequencies of the charge amplifier arewithin the ECG frequency range.

Corner frequencies of the charge amplifier circuit are:

$\begin{matrix}{{f_{a} = \frac{1}{2\pi R_{f}C_{f}}},{and},} & {{Equation}\mspace{14mu} 4} \\{f_{b} = \frac{1}{2\pi R_{s}C_{f}}} & {{Equation}\mspace{14mu} 5}\end{matrix}$

In cases where there is no series capacitance 113 in the circuit, thereis only one corner frequency (lower cut off f_(a)).

Anticipated ECG frequency range is between 0.5 Hz to 150 Hz. ECGcomponents lying within the range of the corner frequencies will beintegrated.

Selections of the values of R_(f), C_(f), Ce′ and R_(s), are made forthe charge amplifier, such as 116, where Ce′ is the capacitance betweenthe surface of the body and the electrode 106 of the sensor 105, makingup part of Ce 113 which includes the capacitance formed by the sensor.

The reader will appreciate that the charge amplifier 114 follows aninverting amplifier configuration, for which the gain can be expressedas follows.

$\begin{matrix}{G = {- \frac{Z_{f}}{Z_{s}}}} & {{Equation}\mspace{11mu} 6}\end{matrix}$

where Z_(f) is the feedback impedance and Z_(s) is the series impedance,provided by Ce′ for example.

The sensing circuitry 109 operates in a regime defined by selections offeedback components and series components of charge amplifier, withfeedback and series components providing feedback and series impedanceswhere the gain determined Equation 6 is great enough to amplify thebiopotential signal above a noise floor and where the feedbackcomponents including a capacitor in parallel with a resistor defining acorner frequency defined by Equation 4 above the biopotential signalfrequency range to not filter out components of the biopotential signaland where the series components are selected to provide a cornerfrequency defined by Equation 5 far enough below the biopotential signalto not filter the lower frequency components of the biopotential signaland selected to also have an impedance which is greater than theanticipated impedance of the connection for the biopotential signalprovided by the sensor receiver. The biopotential signal used in thisfor these selections is a biopotential signal which is anticipated asbeing sensed. Similarly, in this example noise floor may be ananticipated noise floor.

The reader will recognise equivalent regimes with non-invertingamplifiers or with other equivalent circuitry of alternativeembodiments.

FIG. 8 illustrates a sensor, or sensor receiver, 205 according toanother embodiment of the invention. The sensor receiver 205 has firstand second sensor electrodes 208 a and 208 b which are able to formfirst and second signal connections with a body (not shown). Eachelectrode is able to receive the biopotential signal and connect it tothe terminal with an impedance which differs between the first andsecond receivers. The first and second electrodes each lie within asensing periphery 219 which defines a sensing region for thebiopotential signal. Each electrode 208 is assumed to receive the samebiopotential signal in the sensing region via a distinct signalconnection formed with the body by each electrode. Alternatively, thesensing region is dimensioned to the highest spatial resolution at thesurface of the body required for sensing of a biopotential signal.

As shown in FIG. 8, 208 a is a conductive area forming one plate of acapacitor and 208 b is a conductive area electrically isolated from 208a. The reader will appreciate that a conductive area, such as 208 a forexample, will form capacitances with both the body and the othercapacitive area 208 b, for example.

The electrodes 208 a and 208 b each provide an impedance for thebiopotential signal. In the example of FIG. 8 the sensor is capacitive,and the impedance is capacitive as known to the reader. The sensor 205is arranged so that the electrodes each have an impedance with a definedapproximate relationship with each other. For example, a secondelectrode 208 b may provide a second signal connection which has animpedance which is defined by a known relation to the impedance of afirst signal connection provided by the first electrode 208 a. Therelationship may be that the second electrode 208 b is a factor of theimpedance of the impedance provided by the first electrode 208 a. In thespecific example shown the factor is two.

The reader will appreciate that the electrodes do not likely providepurely capacitive connections defined by a scalar separation of theelectrode from an electrode representing the skin.

Therefore, there may be known and unknown impedance parameters if thesignal connection. In these cases the electrodes 208 b will be arrangedto provide a second signal connection which has an unknown impedanceparameter which is defined by a known relation to an unknown impedanceparameter of a first signal connection provided by the first electrode.

In this example the impedance is provided by a capacitance and therelationship between the electrodes 208 a and 208 b is providedsubstantially by the electrode 208 a having an area that is larger by aknown factor. The electrodes 208 a and 208 b are aligned in the sameplane and separated spatially by an insulator 220. In this case theinsulator is an annular sheet of dielectric material. In this case anunknown first impedance parameter of the first signal connection may bea capacitance formed between the first electrode 208 a and a body.Alternatively, an unknown first impedance parameter may be a reactanceof the first signal connection provided by the first electrode 208 a.

FIG. 9 illustrates a sensor device 201 made of a sensor 205, sensingcircuitry 209, a sensing processor 210 able to perform data operationsand connected to the sensor circuitry by a data bus 221. The sensorcircuit receives first and second electrode signals from the first andsecond electrodes 208 a and 208 b and outputs first and second sensorsignals to the bus 221 as channels of a data signal.

The sensor device 201 has the sensor receiver of FIG. 8 with eachelectrode 208 a and 208 b connected to sensing circuitry 209.

A layer of dielectric material 213 is located between the electrodes 208and a surface 202 of a body 203. An air gap 211 is shown between thesensor receiver 205 and the surface 202 to illustrate a gap that mayoccur inadvertently.

The first and second electrode signals received by the sensing circuitry209 are unknown voltages V_(u1) and V_(u2) caused by the samebiopotential signal with first and second sensor impedances formed bydifferent the first electrode and second electrode respectively with thesurface of the body. This is, the sensor receiver provides a connectionto the biopotential signal via a different one of the electrodes 208 aand 208 b and different impedances which have a known relationship witheach other.

As discussed above, the specific example of FIGS. 8 and 9 the connectionfor the biopotential signal is formed by a capacitance between thesurface 202 and the electrode 208 a or 208 b. In the example of FIGS. 8and 9 the area of the electrode 208 a has an area which forms a firstsensor capacitance with the surface 202 that has a defined relationshipwith a second sensor capacitance 208 b. An unknown second capacitance,or other impedance parameter, may be considered dependent on the unknownfirst capacitance by the known relationship. In the specific example ofthis embodiment the defined relationship is that the capacitance formedby the second electrode 208 b is a factor of the capacitance formed bythe first electrode 208 a. In this specific example the factor is two.In the example illustrated with reference to FIGS. 8 and 9 therelationship between the first and second sensor capacitances, or otherunknown impedance parameters associated with these capacitances, isdetermined substantially by the relative areas of the first electrode208 a and the second electrode 208 b. In this example, the sensorreceiver 205 is arranged to provide a similar air gap with the surface202 and each of the electrodes 208 a and 208 b and the sensor receiverhas a similar dielectric material and similar thicknesses of dielectricmaterial between the first electrode and the surface and between thesecond electrode and the surface. Therefore, in this example electrodeshaving areas in which one is a factor of the other will providecapacitances which are approximately the same factor of each other byEquation 1.

The series impedance Z_(a1) between an ideal voltage signal representinga biopotential signal and sensing circuitry 209 will be relatedsimilarly to the relationship of capacitances formed between electrodes208 and the surface 202. The impedance between the biopotential signaland each input 221 a and 221 b of the sensing circuitry 209 will differby approximately the same factor as the area of the capacitances by thefollowing equation for Z_(a), considered as a capacitive impedancedefined by the dimension of the electrode on the sensor.

$\begin{matrix}{Z_{a} = \frac{1}{sC_{a}}} & {{Equation}\mspace{11mu} 7}\end{matrix}$

where C_(a) depends on the electrode size,

$\begin{matrix}{C_{a} = {ɛ_{0}ɛ_{r}\frac{A}{d}}} & {{Equation}\mspace{14mu} 8}\end{matrix}$

ε₀ is the permittivity of free space, 8.85*10⁻¹² F/m, ε_(r) is therelative permittivity of the medium, A is the area of the electrode andd is the thickness of the medium or distance between electrodes formingthe capacitance, such as the surface 202 and an electrode 208 a.

As apparent from Equation 7 the dimension and/or area, A of the secondelectrode 208 b as a multiple of the area of the first electrode 208 aachieves a capacitance of n C_(a), where n is the ratio of the area ofthe two electrodes and Ca is the capacitance formed by the surface 202and the first electrode 208 a.

By Equation 4, substantially a similar multiple of impedances seen by asignal via the second electrode 208 b versus the first electrode 208 acan be arranged.

The processor of the embodiment of FIG. 9 receives a signal from each oftwo channels of the sensing circuitry where each channel applies arespective defined transfer function to the signals received at theelectrodes 208 a and 208 b.

The embodiment illustrated with reference to FIGS. 8 and 9 determinesthe biopotential signal independently of sensor impedances formedbetween the surface 202 and the each of the electrodes 208 a and 208 bsensors. The sensor signal is determined by signals at multiple outputchannels of the sensing circuitry 209, transfer functions for the outputchannels of the sensing circuitry 209 and a defined relationship betweenthe sensor impedances and the defined relationship of the firstelectrode 208 a and second electrode 208 b.

Determining a biopotential signal independently of the impedanceaccording to the invention is illustrated with reference to FIG. 10showing sensing circuitry 309 according to a further embodiment of theinvention. The sensing circuitry 309 may be connected to a sensor 205 asillustrated in FIG. 8 with an electrode 208 a providing a connectionwith impedance Z_(u1) 325 a and with an electrode 208 b providing aconnection with impedance H₁₂ Z_(u1) 325 b.

The sensing circuitry 309 has two charge amplifiers 320 a and 320 bformed of inverting operational amplifier circuits which each provide atransfer function between inputs 321 a and 321 b and outputs 322 a and322 b. The transfer function is defined by feedback impedances Z_(f1)323 a and Z_(f2) 323 b and series impedances Z_(s1) 324 a and Z_(s2) 324b.

The impedances 325 a Z_(u1) shown in FIG. 10 represents an unknownimpedance of a signal connection formed between the surface of a body(not shown) and a first electrode (not shown) of a sensor receiver (notshown). The impedance 325 b H₁₂ Z_(u1) shown in FIG. 10 represents theunknown impedance between the surface of a body and a first electrode(not shown) of a sensor (not shown). In this example the sensor receiveris arranged so that the impedance 325 b is a factor H₁₂ of the impedance325 a. In this example also, the series impedances are illustrated asseparate to impedances 325 a and 325 b formed by the electrode-surfaceinterfaces.

The invention will now be illustrated for example embodiments using twochannels, both channels using inverting amplifiers as receiver circuits,using different unknown impedances related by H12 to represent a signalconnection formed by the sensor device where the impedance may beunknown or variable, and with the processor reading only voltage.

Mitigation, cancellation or nullification of effects involving Z_(u1) orcapacitance, due to an air gap at a sensor-body interface (not shown)according to the embodiment of the invention of FIG. 10 is illustratedbelow.

The equations for the two channel outputs 322 a and 322 b, following theabove circuit, can be defined as:

$\begin{matrix}{{V_{1} = {{- \frac{Z_{f1}}{Z_{s1} + Z_{u\; 1}}}V_{in}}},{and},} & {{Equation}\mspace{14mu} 9} \\{V_{2} = {{- \frac{Z_{f2}}{Z_{s\; 2} + {H_{12}Z_{u\; 1}}}}V_{in}}} & {{Equation}\mspace{14mu} 10}\end{matrix}$

where v_(in), v₁, V₂, are in the frequency domain.

The value of Z_(u1) is unknown and changes with time, however the valueof H₁₂ is known. From equations 9 and 10:

$\begin{matrix}{{{( {V_{1} \times Z_{s1}} ) + ( {V_{1} \times Z_{u\; 1}} )} = {{- Z_{f1}} \times V_{in}}},{{( {V_{2} \times Z_{s2}} ) + ( {V_{2} \times H_{12}Z_{u\; 1}} )} = {{- Z_{f2}} \times V_{in}}}} & {{Equation}\mspace{14mu} 11}\end{matrix}$

Eliminating the value of Z_(u1) and solving equation 11:

$\begin{matrix}{V_{in} = \frac{V_{1}{V_{2}( {{H_{12}Z_{s1}} - Z_{s\; 2}} )}}{{{- H_{12}}V_{2}Z_{f1}} + {V_{1}Z_{f2}}}} & {{Equation}\mspace{14mu} 12}\end{matrix}$

Equation 13 deliberately omitted.

Using Equation 9 input signal V_(in) can be reconstructed from knownparameters V₁, V₂, H₁₂, Z_(s1), Z_(s2), Z_(f1) and Z_(f2).

As the transfer function of the sensing circuitry 309 is in theFrequency domain, V_(in) can be determined by the following steps:

a. Acquiring V₁ and V₂ sampled at a frequency Fs (above 250 Hz for anECG signal)b. Taking a discrete Fourier transform (FFT) of V₁ and V₂.

$\begin{matrix}{{{FFT}( V_{1} )} = {{{\hat{V}}_{1}(k)} = {\sum_{j = 0}^{N - 1}{{V_{1}(j)}e^{{- 2}\;\pi\;{{ikj}/N}}}}}} & {{Equation}\mspace{14mu} 14} \\{{{FFT}( V_{2} )} = {{{\hat{V}}_{2}(k)} = {\sum_{j = 0}^{N - 1}{{V_{2}(j)}e^{{- 2}\;\pi\;{{ikj}/N}}}}}} & {{Equation}\mspace{14mu} 15}\end{matrix}$

Where N is number of samples in V₁ and V₂ and k=0 to N−1, i=sqrt(−1).c. From Equation 12,

$\begin{matrix}{{\hat{V}}_{recon} = \frac{{\hat{V}}_{1}{{\hat{V}}_{2}( {{H_{12}Z_{s\; 1}} - Z_{s\; 2}} )}}{{{- H_{12}}{\hat{V}}_{2}Z_{f\; 1}} + {{\hat{V}}_{1}Z_{f\; 2}}}} & {{Equation}\mspace{14mu} 16}\end{matrix}$

where {circumflex over (V)}_(recon) is the reconstructed ECG infrequency domain.

From Equation 16 it can be inferred that the denominator becomes 0 if

$\begin{matrix}{{\frac{{\hat{V}}_{1}}{{\hat{V}}_{2}} = {{H_{12}\mspace{14mu}{and}\mspace{14mu} Z_{f1}} = Z_{f2}}},{and},} & {{Equation}\mspace{14mu} 17}\end{matrix}$

The numerator becomes 0 if

$\begin{matrix}{\frac{Z_{s\; 2}}{Z_{s\; 1}} = H_{12}} & {{Equation}\mspace{14mu} 18}\end{matrix}$

Therefore, for reconstruction, the following conditions need to besatisfied:

$\begin{matrix}{\frac{{\hat{V}}_{1}}{{\hat{V}}_{2}} \neq {H_{12}\mspace{14mu}{and}\mspace{20mu}\frac{Z_{s\; 2}}{Z_{s\; 1}}} \neq H_{12}} & {{Equation}\mspace{14mu} 19}\end{matrix}$

Taking the inverse Fourier Transform (IFFT) to transform thereconstructed signal from frequency domain to time domain.

$\begin{matrix}{{V_{recon} = {{IFFT}( {\hat{V}}_{recon} )}},{where}} & {{Equation}\mspace{14mu} 20} \\{{{IFFT}( {\hat{V}}_{recon} )} = {{V_{recon}(j)} = {\frac{1}{N}{\sum_{k = 0}^{N - 1}{{{\hat{V}}_{recon}(k)}e^{{- 2}\pi\;{{ikj}/N}}}}}}} & {{Equation}\mspace{14mu} 21}\end{matrix}$

where j=0 to N−1 Adaptions to Equations 9 to 21 for a similar circuitrywith each channel having different Z_(f) values will be apparent to thereader.

Adaptions to Equations 9 to 21 for circuits equivalent and alternativeto an inverting amplifier will also be apparent to the reader.

A process (S1) for determining the biopotential signal carried out by aprocessor 310 of the embodiment of the invention illustrated withreference to FIG. 11 using the approach illustrated in FIG. 11.

The process takes the two channels—V1 and V2 output by sensing circuitry309 and computes the input voltage V_(in) for a biopotential signalthrough the above equations.

At Step S1-1 of the process, signals at each channel of the sensingcircuitry are acquired. In this example V₁ and V₂ are sampled by theprocessor 310 at a sampling frequency Fs. In this example the acquiredsignals are stored in a volatile memory of the processor.

At S1-2 the acquired signals are ‘windowed’, as will be understood bythe reader, to a multiple of the sampling frequency Fs. For example:

$\begin{matrix}{V_{1} = {V_{1}( {{Fs}\text{:}5*{Fs}} )}} & {{Equation}\mspace{14mu} 22}\end{matrix}$

At S1-3 fast Fourier transforms of the sampled signals are computed andstored to provide signals in the frequency domain. For example,

$\begin{matrix}{{\hat{V}}_{1} = {{FFT}( V_{1} )}} & {{Equation}\mspace{14mu} 23} \\{{\hat{V}}_{2} = {{FFT}( V_{2} )}} & {{Equation}\mspace{14mu} 24}\end{matrix}$

At S1-4 point-by-point multiplication of {circumflex over (V)}₁ and{circumflex over (V)}₂ is performed to calculate Î, where:

$\begin{matrix}{\hat{I} = \frac{{\hat{V}}_{1} \times {\hat{V}}_{2}}{{H_{12}{\hat{V}}_{2}} - {\hat{V}}_{1}}} & {{Equation}\mspace{14mu} 25}\end{matrix}$

At S1-5 the Transfer Function of the sensing circuitry is computed.

In one example, corresponding to the sensing circuitry illustrated withreference to FIG. 10, a processor operation equivalent using equation 23is performed using known values of parameters Z_(s)1, Z_(s)2, Z_(f) andH₁₂. The following parameter values are used in this example: Z_(s)1 andZ_(s)2, the series impedances in the channel circuit, comprised ofeither a capacitance per channel C_(e1) and C_(e2) or a resistance witha capacitance in each channel (R_(s1)+C_(e1), R_(s2)+C_(e2)), H₁₂=2

(based on the ratio of area of electrodes which was 2). The range ofR_(s1) and R_(s2) is between 0 to 100 MOhms. C_(e1) and C_(e2) werechosen such that C_(e2)/C_(e1) is not equal to H₁₂. The range of valuesis between 22 pF to 500 pF. Z_(f), the feedback impedance comprises ofresistance R_(fin) parallel with a capacitance C_(f).

The total feedback impedance is:

$\begin{matrix}{Z_{f} = \frac{R_{f}}{1 + {sR_{f}C_{f}}}} & {{Equation}\mspace{14mu} 26}\end{matrix}$

The values of R_(f) and C_(f) were chosen to be 10-50 GOhms and 100-10pF.

At S1-6 the frequency response of transfer function TF(s) is computed asa set of values at each frequency 2.

At S1-7 the reconstructed biopotential signal {circumflex over(V)}_(recon) is determined in the frequency domain by operationsequivalent to:

$\begin{matrix}{{\hat{V}}_{recon} = {{TF} \times \hat{I}}} & {{Equation}\mspace{14mu} 27}\end{matrix}$

At S1-8 the biopotential signal is determined it time domain from thefrequency domain an inverse fast Fourier transform:

$\begin{matrix}{{V_{in}(t)} = {{IFFT}( {\hat{V}}_{recon} )}} & {{Equation}\mspace{14mu} 28}\end{matrix}$

The invention will now be illustrated for embodiments with generalisedreceiver circuits and electrodes.

Various embodiments of the invention may use alternative sensingcircuitry to the charge amplifier operational amplifier circuitryillustrated. The invention using generalised sensing circuitry isillustrated with reference to FIG. 12 by the treatment below.

FIG. 12 illustrates sensing circuitry 409 for sensing a biopotentialsignal sourced by first and second sensing channels (423 a and 423 b)which form connections with the surface of a body (not shown) in asensing region (not shown).

FIG. 12 illustrates an ideal voltage 404 Vin, representing abiopotential signal. Impedances 425 a and 425 b represent first andsecond sensor impedances of first and second sensing channels formedwith the surface of the body (not shown) to receive the biopotentialsignal.

The sensing channels are arranged as illustrated herein so that thefirst and second sensor impedances 425 a and 425 b have substantially adefined relationship

$\begin{matrix}{{{{Zu}\; 1} = {Zu}},{{{Zu}\; 2} = {{H_{12}{Zu}\; 1} + k_{12}}}} & {{Equation}\mspace{14mu} 29}\end{matrix}$

The sensing circuitry 409 a and 409 b provide sensing signals at firstand second outputs 427 a and 427 b. The sensing signals are provideddependent on first and second sensing channel signals received by thecircuitry 409 at first and second sensing terminals 426 a and 426 b.

Consider the sensing circuitry of FIG. 12 representing a general form ofthe proposed measurement system.

The impedances 425 a Z_(u1) and 425 b Z_(u2) are unknown and/orvariable. In the example of the electrodes (not shown) forming acapacitive connection with the surface of the body (not shown), theimpedances Z_(u) may change due to changes in an air gap between theelectrodes and the surface of the body. Also in the example of theelectrodes (not shown) forming a capacitive connection, changes ofpermittivity of any dielectric materials between the electrodes and thebody may change the impedances Z_(u).

The sensing circuitry 409 provides a sensing signals at outputs 427 aand 427 b after a defined transfer function is applied.

The invention will now be illustrated for example embodiments usingtwo-channels, op-amp circuit for the receiver circuits, differentimpedances for the signal connections provided by the sensor electrodes,and the processor measuring voltage and current.

The transfer function may be defined by an operational amplifier circuitwith series impedances Z_(s) and feedback impedances Z_(f).

In this example, series impedances defining transfer functions of eachsensing circuit 409 a and 409 b is Z_(s1) and Z_(s2) respectively.

In this example also, feedback impedances defining transfer functions ofeach sensing circuit 409 a and 409 b are Z_(f1) and Z_(f2) respectively.

In this example, V_(u1) and V_(u2) represent the signal at the inputs426 a and 426 b of the sensing circuits 409 a and 409 b respectively.

Considering the unknown series impedances:

$\begin{matrix}{{V_{in} - V_{u1}} = {i_{u\; 1}Z_{u\; 1}}} & {{Equation}\mspace{14mu} 30} \\{{V_{in} - V_{u2}} = {i_{u\; 2}Z_{u\; 2}}} & {{Equation}\mspace{14mu} 31}\end{matrix}$

where V_(u1) and V_(u2) are the voltages at the inputs 426 a and 426 bafter the unknown series impedance, and i_(u1) and i_(u2) are thecurrents 428 a and 428 b flowing through the unknown impedances and intothe sensing circuits 409 a and 409 b.

Now the sensing device can be generalised by using a transfer functionmatrix TF1 and TF2 for each measurement circuit respectively 409 a and409 b:

Consider the circuit of FIG. 12, representing a general form of sensingcircuitry of various embodiments of the invention.

Considering the unknown series impedance represented by theelectrode-surface interface.

$\begin{matrix}{{V_{in} - V_{u1}} = {i_{u1}Z_{u1}}} & {{Equation}32}\end{matrix}$ $\begin{matrix}{{V_{in} - V_{u2}} = {i_{u2}Z_{u2}}} & {{Equation}33}\end{matrix}$

Where V_(u1) and V_(u2) are signals at the outputs of the first andsecond electrodes with unknown series impedance represented as Z_(u1)425 a and Z_(u2) 425 b, i_(u1) and i_(u2) are the currents flowingthrough the same unknown impedances into the sensing circuitry at inputs426 a and 426 b. Equations 34 to 37 deliberately omitted.

Now the sensing device formed of the sensor, with first and secondelectrodes, and sensing circuitry 409 can be generalised by using atransfer function {TF1, TF2}:

$\begin{matrix}{V_{1} = {{{TF}_{1v}V_{u\; 1}} + {{TF}_{1i}i_{u\; 1}}}} & {{Equation}\mspace{14mu} 38} \\{V_{2} = {{{TF}_{2v}V_{u\; 2}} + {{TF}_{2i}i_{u\; 2}}}} & {{Equation}\mspace{14mu} 39}\end{matrix}$

where V₁ and V₂ are the output voltages, sensing signals or sensingsignal channels, at outputs 427 a and 427 b, which relate linearly tothe input voltages and currents at 426 a and 426 b. We can rewrite thisin matrix form:

$\begin{matrix}{{\begin{pmatrix}1 & 0 & i_{u\; 1} & {- 1} \\0 & 1 & {H_{12}i_{u\; 2}} & {- 1} \\{TF}_{1v} & 0 & 0 & 0 \\0 & {TF}_{2v} & 0 & 0\end{pmatrix} \cdot \begin{pmatrix}V_{u\; 1} \\V_{u\; 2} \\Z_{u\; 1} \\V_{in}\end{pmatrix}} = \begin{pmatrix}0 \\{{- i_{u\; 2}}k_{12}} \\{V_{1} - {i_{u\; 1}{TF}_{1i}}} \\{V_{2} - {i_{u\; 2}{TF}_{2\; i}}}\end{pmatrix}} & {{Equation}\mspace{14mu} 40}\end{matrix}$

Which can be solved using standard linear matrix techniques:

$\begin{matrix}{V_{u\; 1} = \frac{V_{1} - {i_{u\; 1}{TF}_{1i}}}{{TF}_{1v}}} & {{Equation}\mspace{14mu} 41} \\{V_{u\; 2} = \frac{V_{2} - {i_{u\; 2}{TF}_{2i}}}{{TF}_{2v}}} & {{Equation}\mspace{14mu} 42} \\{Z_{u\; 1} = \frac{\begin{matrix}{{( {{- V_{1}} + {i_{u\; 1}{TF}_{1i}}} ){TF}_{2v}} +} \\{{TF}_{1v}( {V_{2} - {i_{u\; 2}{TF}_{2i}} + {i_{u\; 2}k_{12}{TF}_{2v}}} )}\end{matrix}}{( {i_{u\; 1} - {H_{12}i_{u\; 2}}} ){TF}_{1v}{TF}_{2v}}} & {{Equation}\mspace{14mu} 43} \\{V_{in} = \frac{\begin{matrix}{{H_{12}{i_{u\; 2}( {{- V_{1}} + {i_{u\; 1}{TF}_{1i}}} )}{TF}_{2v}} +} \\{i_{u\; 1}{{TF}_{1v}( {V_{2} - {i_{u\; 2}{TF}_{2i}} + {i_{u\; 2}k_{12}{TF}_{2v}}} )}}\end{matrix}}{( {i_{u\; 1} - {H_{12}i_{u\; 2}}} ){TF}_{1v}{TF}_{2v}}} & {{Equation}\mspace{14mu} 44}\end{matrix}$

We see that the unknown input voltage V_(in) can be estimated bymeasuring both output voltages and input currents.

The invention will now be illustrated with example embodiments usingtwo-channels, generalized circuit for the receiver circuits, the samesigna connection for each channel, and the processor measuring currentand voltage.

If both unknown sensor impedances are the same, then:

$\begin{matrix}{ H_{12}arrow 1 ; k_{12}arrow 0 } & {{Equation}\mspace{14mu} 45} \\{V_{u\; 1} = \frac{V_{1} - {i_{u\; 1}{TF}_{1i}}}{{TF}_{1v}}} & {{Equation}\mspace{14mu} 46} \\{V_{u\; 2} = \frac{V_{2} - {i_{u\; 2}{TF}_{2i}}}{{TF}_{2v}}} & {{Equation}\mspace{14mu} 47} \\{Z_{u\; 1} = \frac{{{TF}_{1v}( {V_{2} - {i_{u\; 2}{TF}_{2i}}} )} + {( {{- V_{1}} + {i_{u\; 1}{TF}_{1i}}} ){TF}_{2v}}}{( {i_{u\; 1} - i_{u\; 2}} ){TF}_{1v}{TF}_{2v}}} & {{Equation}\mspace{14mu} 48} \\{V_{in} = \frac{{i_{u\; 1}{{TF}_{1v}( {V_{2} - {i_{u\; 2}{TF}_{2i}}} )}} + {{i_{u\; 2}( {{- V_{1}} + {i_{u\; 1}{TF}_{1i}}} )}{TF}_{2v}}}{( {i_{u\; 1} - i_{u\; 2}} ){TF}_{1v}{TF}_{2v}}} & {{Equation}\mspace{14mu} 49}\end{matrix}$

Note that when H₁₂=1 and k₁₂=0 there is a requirement that:

$\begin{matrix}{i_{u1} \neq i_{u2}} & {{Equation}62}\end{matrix}$

which implies a constraint on the circuits that the two input impedancesmust be different and/or the gains of sensing circuitry 409 a and 409 bmust be different.

Below are illustrated various circuits representing the body, sensorelectrodes, and sensing circuits.

The invention will now be illustrated with example embodiments usingtwo-channels, both using inverting amplifiers as receiver circuits,having different impedances for the signal connections, and with theprocessor reading both voltage and current.

In one embodiment the sensing circuits may be in the class of invertingamplifiers. We can represent this class of circuit with no gain due toinput current, and the amplifier gain is given by:

$\begin{matrix}{ {TF}_{1i}arrow 0 , {TF}_{2i}arrow 0 , {TF}_{1v}arrow{- \frac{Z_{f\; 1}}{Z_{s\; 1}}} , {TF}_{2v}arrow{- \frac{Z_{f\; 2}}{Z_{s\; 2}}} } & {{Equation}\mspace{14mu} 50} \\{V_{u\; 1} = \frac{{- V_{1}}Z_{s\; 1}}{Z_{f\; 1}}} & {{Equation}\mspace{14mu} 51} \\{V_{u\; 2} = \frac{{- V_{2}}Z_{s\; 2}}{Z_{f\; 2}}} & {{Equation}\mspace{14mu} 52} \\{Z_{u\; 1} = \frac{{i_{u\; 2}k_{12}Z_{f\; 1}Z_{f\; 2}} + {V_{1}Z_{f\; 2}Z_{s\; 1}} - {V_{2}Z_{f\; 1}Z_{s\; 2}}}{{i_{u\; 1}Z_{f\; 1}Z_{f\; 2}} - {H_{12}i_{u\; 2}Z_{f\; 1}Z_{f\; 2}}}} & {{Equation}\mspace{14mu} 53} \\{V_{in} = \frac{\begin{matrix}{{i_{u\; 1}i_{u\; 2}k_{12}Z_{f\; 1}Z_{f\; 2}} + {H_{12}i_{u\; 2}V_{1}Z_{f\; 2}Z_{s\; 1}} -} \\{i_{u\; 1}V_{2}Z_{f\; 1}Z_{s\; 2}}\end{matrix}}{{i_{u\; 1}Z_{f\; 1}Z_{f\; 2}} - {H_{12}i_{u\; 2}Z_{f\; 1}Z_{f\; 2}}}} & {{Equation}\mspace{14mu} 54}\end{matrix}$

where Z_(f1) and Z_(f2) are in the feedback path for 409 a and 409 b,and Z_(s1) and Z_(s2) are in the input path.

The invention will now be illustrated with example embodiments usingtwo-channels, both including inverting amplifiers as receiver circuits,using different impedances for the signal connection, and with theprocessor reading only voltage.

In addition, for an inverting amplifier

$\begin{matrix}{{{- V_{1}} + V_{u\; 1}} = {i_{u\; 1}( {Z_{f\; 1} + Z_{s\; 1}} )}} & {{Equation}\mspace{14mu} 55} \\{{{- V_{2}} + V_{u\; 2}} = {i_{u\; 2}( {Z_{f\; 2} + Z_{s\; 2}} )}} & {{Equation}\mspace{14mu} 56}\end{matrix}$

Equations 57 to 60 deliberately omitted.

We can therefore eliminate i_(u1) and i_(u2) from the above equations:

Solving for V_(in):

$\begin{matrix}{V_{in} = {- \frac{V_{1}{V_{2}( {k_{12} - {H_{12}Z_{s\; 1}} + Z_{s\; 2}} )}}{{{- H_{12}}V_{2}Z_{f\; 1}} + {V_{1}Z_{f\; 2}}}}} & {{Equation}\mspace{14mu} 61}\end{matrix}$

The invention will now be illustrated with example embodiments using twochannel, both including non-inverting amplifiers as receiver circuits,having the same impedance for the signal connection and the processorreading only voltage.

In another embodiment the sensing circuits may be in the class ofnon-inverting amplifiers, when H₁₂=1 and k₁₂=0.

$\begin{matrix}{ {{TF}\; 1_{i}}arrow 0 , {{TF}\; 2_{i}}arrow 0 , {{TF}\; 1_{v}}arrow{1 + \frac{Z_{f\; 1}}{Z_{s\; 1}}} , {{TF}\; 2_{v}}arrow{1 + \frac{Z_{f\; 2}}{Z_{s\; 2}}} } & {{Equation}\mspace{14mu} 610}\end{matrix}$

So that the channel transfer functions are

$\begin{matrix}{V_{1} = {( {1 + \frac{Z_{f1}}{Z_{1}}} )V_{in}}} & {{Equation}\mspace{14mu} 611} \\{V_{2} = {( {1 + \frac{Z_{f2}}{Z_{2}}} )V_{in}}} & {{Equation}\mspace{14mu} 612}\end{matrix}$

The biopotential can be reconstructed from

$\begin{matrix}{V_{in} = \frac{{i_{u\; 1}V_{2}{Z_{2}( {Z_{1} + Z_{f\; 1}} )}} - {H_{12}i_{u\; 2}V_{1}{Z_{1}( {Z_{2} + Z_{f\; 2}} )}}}{( {i_{u\; 1} - {H_{12}i_{u\; 2}}} )( {Z_{1} + Z_{f\; 1}} )( {Z_{2} + Z_{f\; 2}} )}} & {{Equation}\mspace{14mu} 613}\end{matrix}$

Note that eliminating i_(u1) and i_(u2) using the full set of equationsabove is possible

$\begin{matrix}{{V_{1}Z_{1}Z_{s1}} = {{V_{in}( {Z_{1} + Z_{f1}} )}Z_{s1}}} & {{Equation}63}\end{matrix}$ $\begin{matrix}{{V_{2}Z_{2}Z_{s2}} = {{V_{in}( {Z_{s2} + Z_{f2}} )}Z_{s2}}} & {{Equation}64}\end{matrix}$ $\begin{matrix}{{Z_{s1} + Z_{f1}} \neq 0} & {{Equation}65}\end{matrix}$ $\begin{matrix}{{Z_{s2} + Z_{f2}} \neq 0} & {{Equation}66}\end{matrix}$ $\begin{matrix}{{Z_{s1}Z_{s2}} = 0} & {{Equation}660}\end{matrix}$

But the third constraint of Equation 660 is unachievable, even thoughsolutions for Vin exist:

$\begin{matrix}{V_{in} = \frac{V_{1}Z_{1}}{Z_{1} + Z_{f\; 1}}} & {{Equation}\mspace{14mu} 67} \\{V_{in} = \frac{V_{2}Z_{2}}{Z_{2} + Z_{f\; 2}}} & {{Equation}\mspace{14mu} 68}\end{matrix}$

However, the biopotential can be reconstructed if the input impedance ofa practically implemented operational amplifier is considered.

The invention will now be illustrated with example embodiments havingusing two channels, one inverting and one non-inverting amplifier, usingthe same signal connection impedance, and the processor measuring bothinput current and voltage.

In various other embodiments the sensing circuits are an inverting(circuit 1) and non-inverting (circuit 2) amplifier. Then:

$\begin{matrix}{{{TF}\; 1_{2}},{ {{TF}\; 2_{2}}arrow 0 ; {{TF}\; 1_{1}}arrow{- \frac{Z_{f\; 1}}{Z_{{in}\; 1}}} ; {{TF}\; 2_{1}}arrow{1 + \frac{Z_{f\; 2}}{Z_{s\; 2}}} }} & {{Equation}\mspace{14mu} 69} \\{V_{u\; 1} = \frac{{- V_{1}}Z_{s\; 1}}{Z_{f\; 1}}} & {{Equation}\mspace{14mu} 70} \\{V_{u\; 2} = \frac{V_{1}}{1 + \frac{Z_{f\; 2}}{Z_{s\; 2}}}} & {{Equation}\mspace{14mu} 71} \\{Z_{u\; 1} = \frac{{V_{2}Z_{2}Z_{f\; 1}} + {{V_{1}( {Z_{2} + Z_{f\; 2}} )}Z_{s\; 1}}}{( {i_{u\; 1} - i_{u\; 2}} ){Z_{f\; 1}( {Z_{2} + Z_{f\; 2}} )}}} & {{Equation}\mspace{14mu} 72} \\{V_{in} = \frac{{i_{u\; 1}V_{s}Z_{2}Z_{f\; 1}} + {i_{u\; 2}{V_{1\;}( {Z_{2} + Z_{f\; 2}} )}Z_{s\; 1}}}{( {i_{u\; 1} - i_{u\; 2}} ){Z_{f\; 1}( {Z_{2} + Z_{f\; 2}} )}}} & {{Equation}\mspace{14mu} 73}\end{matrix}$

The invention will now be illustrated with example embodiments havingtwo channels, one an inverting amplifier and one non-invertingamplifier, using the same signal connection impedance, and where theprocessor reads only voltage.

In addition, we know that for a real non-inverting amplifier there is aninput impedance:

$\begin{matrix}{{{- V_{1}} + V_{u\; 1}} = {i_{u\; 1}( {Z_{f\; 1} + Z_{s\; 1}} )}} & {{Equation}\mspace{14mu} 74} \\{{{{- V_{2}}\frac{Z_{2}}{Z_{2} + Z_{f\; 2}}} + V_{u\; 2}} = {i_{u\; 2}Z_{s\; 2}}} & {{Equation}\mspace{14mu} 75}\end{matrix}$

We can therefore eliminate V_(u1), V_(u2) and Z_(u) from the aboveequations:

$\begin{matrix}{{{i_{u\; 1}V_{2}Z_{2}} + \frac{{i_{u\; 2}( {Z_{2} + Z_{f\; 2}} )}( {{V_{in}Z_{f\; 1}} + V_{s\; 1}} )}{Z_{f\; 1}}} = {i_{u\; 1}{V_{in}( {Z_{2} + Z_{f\; 2}} )}}} & {{Equation}\mspace{14mu} 76} \\{\frac{\begin{matrix}{{i_{u\; 1}{Z_{f\; 1}( {{V_{2}Z_{2}} - {V_{in}( {Z_{2} + Z_{f\; 2}} )}} )}} +} \\{{i_{u\; 2}( {Z_{2} + Z_{f\; 2}} )}( {{V_{in}Z_{f\; 1}} + {V_{1}Z_{s\; 1}}} )}\end{matrix}}{( {i_{u\; 1} - i_{u\; 2}} )Z_{f\; 1}} = 0} & {{Equation}\mspace{14mu} 77} \\{i_{u\; 1} \neq i_{u\; 2}} & {{Equation}\mspace{14mu} 78} \\{Z_{f\; 1} \neq 0} & {{Equation}\mspace{14mu} 79} \\{{Z_{2} + Z_{f\; 2}} \neq 0} & {{Equation}\mspace{14mu} 80}\end{matrix}$

This also removes dependency on Z_(s2) i.e. the input impedance of thenon-inverting Op-Amp. The constraints are achievable, and we can findV_(in):

$\begin{matrix}{V_{in} = \frac{{i_{u\; 1}V_{2}Z_{2}Z_{f\; 1}} + {i_{u\; 2}{V_{1}( {Z_{2} + Z_{f\; 2}} )}Z_{s\; 1}}}{( {i_{u\; 1} - i_{u\; 2}} ){Z_{f\; 1}( {Z_{2} + Z_{f\; 2}} )}}} & {{Equation}\mspace{14mu} 81}\end{matrix}$

The invention will now be illustrated with example embodiments havingtwo channels, both differential amplifiers, different impedances for thesignal connections of each channel, and where the processor reads onlyvoltage.

In various other embodiments the sensing circuits are differentialamplifiers. Then:

$\begin{matrix}{ {TF}_{1i}arrow 0 , {TF}_{2i}arrow 0 , {TF}_{1v}arrow\frac{( {Z_{11} + Z_{31}} )Z_{41}}{Z_{11}( {Z_{21} + Z_{41}} )} , {TF}_{2v}arrow\frac{( {Z_{12} + Z_{32}} )Z_{42}}{Z_{12}( {Z_{22} + Z_{42}} )} , i_{u\; 1}arrow\frac{V_{1}Z_{11}}{( {Z_{11} + Z_{31}} )Z_{41}} , i_{u\; 2}arrow\frac{V_{2}Z_{12}}{( {Z_{12} + Z_{32}} )Z_{42}} } & {{Equation}\mspace{14mu} 701}\end{matrix}$

The channel transfer functions are

$\begin{matrix}{V_{1} = {\frac{Z_{41}}{Z_{21} + Z_{41}}\frac{( {Z_{11} + Z_{31}} )}{Z_{11}}V_{in}}} & {{Equation}\mspace{14mu} 82} \\{V_{2} = {\frac{Z_{42}}{Z_{22} + Z_{42}}\frac{( {Z_{12} + Z_{32}} )}{Z_{12}}V_{in}}} & {{Equation}\mspace{14mu} 83}\end{matrix}$

and the biopotential signal is reconstructed as

$\begin{matrix}{V_{in} = \frac{V_{1}V_{2}Z_{11}{Z_{12}( {k_{12} + Z_{22} - {H_{12}( {Z_{21} + Z_{41}} )} + Z_{42}} )}}{{{- H_{12}}V_{2}{Z_{12}( {Z_{11} + Z_{31}} )}Z_{41}} + {V_{1}{Z_{11}( {Z_{12} + Z_{32}} )}Z_{42}}}} & {{Equation}84}\end{matrix}$

The invention will now be illustrated with example embodiments havingmultiple-channels, linear transfer functions, different impedances forthe signal connection from the body to each channel, and where theprocessor reads voltage and current.

The transfer function for the sensing circuitry of FIG. 12 with multipleinput channels each having a transfer function

$\begin{matrix}{V_{n} = {{i_{un}{TF}_{ni}} + {V_{in}{TF}_{nv}} - {i_{un}Z_{un}{TF}_{nv}}}} & {{Equation}85}\end{matrix}$

where

$\begin{matrix}{Z_{un} = {k_{1n} + {H_{1n}Z_{u\; 1}}}} & {{Equation}\mspace{14mu} 86}\end{matrix}$

can be expressed in matrix form.

$\begin{matrix}{{\begin{pmatrix}{TF}_{1v} & {{- i_{\;{u\; 1}}}{TF}_{1v}} \\{TF}_{2v} & {{- H_{12}}i_{u\; 2}{TF}_{2v}} \\\vdots & \vdots \\{TF}_{nv} & {{- H_{1n}}i_{un}{TF}_{nv}}\end{pmatrix} \cdot \begin{pmatrix}V_{in} \\Z_{u\; 1}\end{pmatrix}} = \begin{pmatrix}{V_{1} - {i_{u\; 1}{TF}_{1i}}} \\{V_{2} - {i_{u\; 2}{TF}_{2i}} + {i_{u\; 2}k_{12}{TF}_{2v}}} \\\vdots \\{V_{n} - {i_{un}{TF}_{ni}} + {i_{un}k_{1n}{TF}_{nv}}}\end{pmatrix}} & {{Equation}\mspace{14mu} 87}\end{matrix}$

In the embodiment illustrated with reference to FIG. 8, to give oneexample, the linear relationship between Z_(u1) and Z_(u2) is arrangedby first and second signal channels being arranged to form a linearrelationship of impedances with the body.

Equations 88 to 94 deliberately omitted.

This equation can be solved using linear algebra known to the reader.

$\begin{matrix}{\begin{pmatrix}V_{in} \\Z_{u\; 1}\end{pmatrix} = {\begin{pmatrix}{TF}_{1v} & {{- i_{\;{u\; 1}}}{TF}_{1v}} \\{TF}_{2v} & {{- H_{12}}i_{u\; 2}{TF}_{2v}} \\\vdots & \vdots \\{TF}_{nv} & {{- H_{1n}}i_{un}{TF}_{nv}}\end{pmatrix}^{+}\begin{pmatrix}{V_{1} - {i_{u\; 1}{TF}_{1i}}} \\{V_{2} - {i_{u\; 2}{TF}_{2i}} + {i_{u\; 2}k_{12}{TF}_{2v}}} \\\vdots \\{V_{n} - {i_{un}{TF}_{ni}} + {i_{un}k_{1n}{TF}_{nv}}}\end{pmatrix}}} & {{Equation}\mspace{14mu} 95}\end{matrix}$

In one embodiment a processor similar to 310 determines Vin (thebiopotential signal) from TF₁v, TF₂v, TF₁i, TF_(2i), i_(u1), i_(u2),H₁₂, k₁₂, V₁ (first sensor signal), V₂ (second sensor channel) using aform of Equation 95 from which Z_(u1) has been algebraically eliminated.

FIG. 13 illustrates two embodiments of the invention. FIG. 13illustrates generally the problem of capturing a biopotential signal 504at the surface of a body 503 when the sensor receiver 508 available toform a connection to the body forms a signal connection for thebiopotential signal 504 that has an unknown impedance parameter. A firstsignal channel 511 a is provided to receive a signal at a first channeloutput. However, a first transfer function of the first channel willdepend on the unknown impedance parameter, referred to here as theunknown first impedance parameter. The impedance parameter may be anunknown resistance or reactance, a component of these or a combinationof these. For example, the sensor receiver 508 may form a signalconnection with an unknown impedance parameter formed by a resistance inparallel with a capacitance. The first transfer function will alsodepend on parameters of an circuit 513 a with its own transfer functionand with known component values. In one example this apparatus may be acharge amplifier with known series and feedback component parameters.

The signal at the first channel output may be expressed as

$\begin{matrix}{V_{1} = {f\; 1( {V_{in},z_{u1}} )}} & {{Equation}\mspace{14mu} 96}\end{matrix}$

where V_(in) is the biopotential signal, Z_(u1) is the unknown firstimpedance parameter and f1 is the transfer function. V1 depends on thefirst unknown impedance parameter and therefore cannot be determined.

FIG. 13 shows a second signal channel 511 b arranged to capture the samebiopotential signal 504. The second channel 511 b has a second transferfunction and a second signal output. The second transfer function ofthis embodiment also depends on the first unknown impedance parameter byreceiving the biopotential signal via an electrode 508 b that forms asignal connection with an unknown impedance parameter that is defined bya known relation to the unknown impedance parameter signal connection ofthe electrode 508 a. The second transfer function also depends on atransfer function of a second channel circuit 513 b.

The first and second signal channels 511 a and 511 b therefore share thesame unknown first impedance parameter.

This allows the system to be described by a set of two relations, orequations, for the biopotential signal dependent on each signal channeldependent and on the unknown first impedance parameter. A solution canthen be found for the bipotential signal 504.

Therefore the embodiment of FIG. 13 provides a sensor device having asensor receiver 508 that forms a signal connection for the biopotentialsignal 504 with a first signal channel 511 a and a second signal channel511 b where the system can be describes as a set of mathematicalrelations which depend on the firsts transfer function of the firstsignal channel, or the transfer function of the apparatus 513 a, whichalso depend on the second transfer function of the second signal channel511 b, and which also depends on the first unknown impedance parameter.

As discussed above the first and second signal channels share the samefirst unknown impedance parameter. In the embodiment shown in FIG. 13this sharing is achieved with a sensor receiver 508 which has first andsecond sensor electrodes 506 a and 506 b which each form part of thefirst and second signal channels respectively along with first andsecond channel circuits which each have a known transfer function andknown components which form the respective transfer functions. In thisembodiment the electrodes have a known relationship for unknownimpedance parameters. This is, the unknown second impedance parametercan be defined by a known relation dependent on the unknown firstimpedance parameter. Therefore, the system has a first unknown impedanceparameter Zu1 which is associated with the electrode of the first signalchannel 511 a and second unknown impedance associated Zu2 with thesecond signal channel 511 b. Here, the second transfer function of thesecond signal channel 511 b has been arranged to depend specifically onan unknown second impedance parameter which has a known relationshipwith the unknown first impedance parameter.

As discussed above, the first and second signal channels share the samefirst unknown impedance parameter. FIG. 14 shows an alternativeembodiment which archives the first and second signal channels sharingthe same first unknown impedance parameter by providing first and secondsignal channels 611 a and 611 b including the same sensor electrode 608.In this embodiment the same electrode 608 is connected via a switch 614which switches between devices 613 a and 613 b to connect the sensorreceiver 608 and electrode 608 alternately to form part of the firstsignal channel 611 a and part of the second signal channel 611 b.

In overview with respect to the embodiments of FIG. 13 and FIG. 14, theoriginal biopotential and the unknown impedance can be conceptualised astwo unknown variables: an unknown input and unknown impedance parameter,respectively. A measurement channel can be described with an equationthat relates the unknown input, unknown parameter and measured(therefore, known) output. By itself, this is a system of two unknownsand one equation, which cannot be solved (Equation 96).

Introducing a second signal channel introduces the corresponding numberof equations, or relations for the biopotential signal; so two signal,or measurement, channels allows a solution (two equations, twounknowns), as long as the unknown impedance parameter is shared by bothmeasurement channels.

$\begin{matrix}{V_{2} = {f2( {V_{in},Z_{u2}} )}} & {{Equation}97}\end{matrix}$

This sharing of the parameter can be achieved in at least two ways:

1. A second unknown impedance can be related by a known factor to thefirst unknown impedance e.g.

$\begin{matrix}{{Z_{u\; 2} = {n\mspace{11mu} Z_{u\; 1}}};{V_{2} = {f\; 2( {V_{in},{n\mspace{11mu} Z_{u\; 1}}} )}}} & {{Equation}\mspace{14mu} 98}\end{matrix}$

2. We can switch between the two measurement channels, while keeping thesame unknown impedance e.g.

$\begin{matrix}{V_{2} = {f2( {V_{in},Z_{u1}} )}} & {{Equation}99}\end{matrix}$

It is important that the equation corresponding to the secondmeasurement channel cannot reduce to the equation corresponding to thefirst measurement channel. In the case of the measurement circuitsproposed, this is achieved because output voltages are non-linearlyrelated to unknown impedance:

$\begin{matrix}{V_{1} = \frac{G\mspace{14mu} V_{in}}{Z_{1} + Z_{u\; 1}}} & {{Equation}\mspace{14mu} 100}\end{matrix}$

where G and Z are parameters known from chosen electrical componentvalues.

Further and additional embodiments of the invention will now beillustrated.

Embodiments of the invention provide an apparatus which generates areconstructed biopotential signal sensed at a surface of a body using asensor device which address a problem of impedance of signal connectionsbetween a body and a sensor device having unknown and/or variableimpedance by providing two or more channels between the body and outputsfor a processor where the channels each have a transfer function whichthe impedance through a sensor device and an interface between the bodyand the sensor device where the channels are arranged so that theunknown and/or variable impedance of one channel is related to theunknown and/or variable impedance of the other channel by a lineardefined relationship and where the channels provide two or more transferfunctions for an assumed same bipotential signal to two or more signaloutputs for the processor so that operations equivalent to equatinganalytic expressions of the transfer functions and substituting oneunknown and/or variable impedance for the other will eliminate theunknown and/or variable impedances and will allow the biopotentialsignal to be reconstructed independently of artefacts of the body-sensorinterface or sensor. Biopotential signals can be captured with a varietyof artefacts mitigated and/or eliminated. Such artefacts may be causedby a variation between given implementations in the capacitive and/orresistive impedance of the body-sensor interface, such as might resultby different materials being between a body and a sensor or by differentsensors as required for given applications. Such artefacts may be causedby variations in the capacitive and/or resistive impedance over time,such as caused by movement of a body or movement of the sensor relativeto the body. Such artefacts may be caused by capacitive (imaginary)impedance, resistive (real impedance) or real and imaginary (compleximpedance). In some embodiments the relationship of sensor impedances ofrespective channels may be arranged by two distinct sensor electrodesand differing properties of those or the arrangement of electrode andbody interface. In some embodiments the relationship of sensorimpedances of respective channels may be arranged by a single electrodewith a connection switched between two or more channels.

The reader will appreciate that impedance is frequency dependent.

The reader will appreciate that various of the above equations containvariables in the frequency domain.

In various embodiments more than two sensor electrode pathways can besolved in a least-squares sense, or by other or other optimisation knownto the reader, by adding rows to the above matrix equation.

In various embodiments an electrode is used to provide a first signalconnection to receive a biopotential signal from the body and a receivercircuit to provide a first signal channel comprising the signalconnection combined with the receiver circuit where a first analyticexpression will define the biopotential signal dependent on an impedanceof the first signal connection, on impedances of the receiver circuitand on outputs of the receiver circuitry.

In various embodiments an electrode is used to provide a second signalconnection to receive the same biopotential signal from the body and areceiver circuit to provide a second signal channel comprising thesignal connection combined with the receiver circuit where a secondanalytic expression will define the biopotential signal dependent on animpedance of the second signal connection, on impedances of the receivercircuit and on outputs of the receiver circuitry.

In various embodiments the electrodes are arranged to provide a definedexpression relating the impedance of the first and second signalconnections.

In various embodiments the biopotential signal can be determined usingan expression which is derived by operations on the first analyticexpression, the second analytic expression and the impedance expression,wherein the operations eliminate the impedance of the first and secondsignal connections.

In various embodiments the operations comprise steps equivalent to usingthe impedance expression to eliminate the impedance of the second signalconnection.

In various embodiments the operations comprise steps equivalent toequating the first and second analytic expressions.

In various embodiments the operations may comprise equivalent Gaussianelimination.

The outputs of a receiver circuit may be voltages and/or currents and/orvoltages representing currents.

In various embodiments a sensing processor may stand-alone from thesensing circuitry and may not have a direct electrical connection to thesensing circuitry. In some of these embodiments signals from the sensingcircuitry may be transmitted to the sensing processor. In otherembodiments sensing circuitry may be operable to store signals on areadable medium which is readable by the sensing processor.

In various embodiments determining the biopotential signal independentlyof an impedance between the surface of the body and a sensor receiver,with first and second electrodes, relies on a defined relationshipbetween approximations of real capacitive sensors. For example, thedefined relationship may be for electrode area with a real sensorforming a capacitance between first and second electrodes and a surfaceof a body may be approximated as first and second capacitors. The readerwill appreciate that this or similar approximations will mitigate theeffect of changes in capacitances between the sensor receiver and thesurface of a body. This is particularly but not exclusively where agiven effect for capacitance apply to each capacitance formed betweenthe surface and an electrode.

In various embodiments of the invention a sensor receiver may besubstituted for one or more signal pick-ups. In various embodiments theone or more signal pick-ups may be formed of one or more elements.

In various embodiments electrodes used to capture biopotential signalsmay be provided by multiple elements providing the function of thesensor receiver illustrated.

In various alternative embodiments of the invention a multiple electrodesensing pick-up, such as the multiple electrode element illustrated withreference to FIG. 8 may have more than two electrodes.

In various alternative embodiments of the invention a multiple electrodesensing pick-up, such as illustrated with reference to FIG. 8, may havetwo or more electrodes which provide impedances for the biopotentialsignal that differ according to a defined relationship other than afactor of each other. In various embodiments the relationship ofimpedances of electrodes of a sensor receiver may be as defined by anysuitable expression known to the reader, including factors, orpolynomials.

In various embodiments, alternative to that illustrated with referenceto FIG. 8, the impedance provided by an electrode may be resistive. Oneor more electrodes of these embodiments may make a direct electricallyconductive connection with the surface of the body.

In various embodiments, alternative to that illustrated with referenceto FIG. 8, the impedance provided by an electrode may be inductive.

In various embodiments, alternative to that illustrated with referenceto FIG. 8, the impedance provided by an electrode may a resistance.

In various embodiments, alternative to that illustrated with referenceto FIG. 8, the impedance provided by an electrode may be reactance.

In various embodiments, alternative to that illustrated with referenceto FIG. 8, the impedance provided by an electrode may be resistance anda reactance.

In various embodiments a channel for a signal may be a channel for adata signal. In various embodiments a data signal may be a transmitteddata signal. In various embodiments a data signal may be a stored datasignal. A data signal may be a digitised signal derived from an analoguesignal.

In various embodiments any combination of individual steps illustratedwith reference to FIG. 11 are taken.

In various alternative embodiments acquired signals are stored in anon-volatile memory of the processor.

In various alternative embodiments acquired signals are stored using aprocessor and/or computer readable medium.

In various embodiments first and second sensing signals output fromsensing circuitry may be provided as first and second channels of asensing signal. In various embodiments the sensing signals output bysensing circuitry or used by a sensing processor may be analoguesignals. In other embodiments the sensing the sensing signals output bysensing circuitry or used by a sensing processor may be digitallyencoded signals.

In various embodiments a sensor provides a connection at a surface ofthe body. In various embodiments the connection is a connection for asignal. In some embodiments the sensor provides a capacitive connection.In various embodiments the sensor provides a conductive connection. Invarious embodiments the sensor provides an inductive connection.

Various embodiments have sensors which provide any connection known tothe reader suitable to allow the sensing device to receive abiopotential signal. The reader may recognise the sensing connection asa pick-up connection.

In various embodiments a biopotential signal is sensed as a signal whichhas one of more characteristics of an electrical signal within the bodyor available at the surface of the body. In various embodiments abiopotential signal may be a voltage signal.

In various alternative embodiments the first and second electrodes mayhave inductances which contribute to a defined relationship ofimpedances.

Some embodiments of the invention provide a capacitive connection for abiopotential signal to the surface of a body that may have advantagesover a direct resistive or conducting connection. In one example anadvantage of longevity of connection is provided. On one specificexample an advantage of longevity is achieved when a sensor is requiredto be located on, or affixed to, the skin of a biological subject. In aspecific example again, the sensor can be affixed by a biologicallycompatible adhesive, or other affixing or locating means, that is notrequired to be conductive. However, a capacitive connection with a knownand stable capacitance is difficult to achieve. One effect that may varycapacitance is a variation of the air gap between a sensor receiver andthe surface of the body. This variation may be spatially over a sensingregion or periodically and temporally with movement or contortion of thesubject or temporally with degradation of adhesives, for example, usedto affix the sensor to the subject. These effects are particularlyapparent with a biological subject.

In various embodiments an adhesive used to adhere the sensor to asurface, such as skin is arranged on the sensor between the sensor andthe surface to adhere the sensor directly. In other embodiments a layerof adhesive material may be arranged on an opposite side of the sensorto the surface and extending beyond the sensor to adhere to the surfaceand hold the sensor at the surface.

The reader may recognise a capacitive connection provided by sensors asan electrostatic connection. The reader may recognise a resistiveconnection as a galvanic connection.

In various additional embodiments it is not essential that theimpedances formed by first and second sensor electrodes with the bodyprecisely fit a defined relationship. In these embodiments, variationsfrom a defined relationship may cause an error in a biopotential signaldetermined. In various applications varying degrees of effort may beacceptable as will be apparent to the reader.

In various embodiments processes implemented to carry out operationsillustrated above using mathematical or algebraic expressions,relations, relationships or equations, by performing computational ordata operations on data or code carrying information describing thealgebraic expressions, relations, relationships or equations.

In various embodiments processes implemented to carry out operationsillustrated above using mathematical or algebraic expressions,relations, relationships or equations, by performing any suitablecomputational or data operations known to the reader such as, to namesome examples only, read, write erase, polling, floating pointoperations, scalar, vector or matrix operations such as multiplication,and addition.

In some embodiments, first and second sensor receivers share anelectrode. The electrode may form a capacitive connection for thebiopotential signal. Alternatively, the electrode may form a conductiveconnection for the biopotential signal. Alternatively, the electrode mayform a combination capacitive and conductive connection for thebiopotential signal.

In the preceding description and the following claims, the word“comprise” or variations thereof is used in an inclusive sense tospecify the presence of the stated feature or features. This term doesnot preclude the presence or addition of further features in variousembodiments.

In the preceding description and the following claims, the word “a” isnot intended to exclude “another” “a second”, a “plurality” or similarexpressions.

As used herein the term ‘capture’ refers broadly to capturing a signalor data which carries information on the biopotential signal, and mayinclude, to name examples, generating a signal and generating datacarrying information on a signal.

As used herein the term ‘electrode’ refers broadly to a conductorthrough which electricity enters or leaves a circuit, wire, rail,channel, object, substance, or region and explicitly includes caseswhere the electricity enters or leaves by conductive connections formedby the conductor and/or capacitive connections formed by the conductor.

As used herein the term ‘parameter’ refers broadly to any numerical orother measurable factor forming one of a set that defines a system orsets the conditions of its operation, and may for example refer toimpedance, resistance, reactance, any combination of these.

As used herein the term ‘channel’ refers broadly to a path for anelectric signal.

As used herein the term ‘relation’ refers broadly to anything whichdefines relationships between values or parameters and a relation may beexpressed in text, data, matrices, vectors, tables and data, media ormemory carrying information on these.

As used herein the term ‘dependent on’, ‘depends on’ or similar used inreference to a parameter or value, for example, and a relation orexpression refers to the parameter or value being a variable in therelation or expression. For example a

As used herein the term ‘biopotential signal’ refers broadly to anelectrical signal measures at, on or in biological bodies, and includeselectrical signals (voltages) that are generated by physiologicalprocesses occurring within the body.

As used herein the term ‘sensing’ refers broadly to detecting andidentifying a signal and characteristics of the signal such asparameters which define the signal over time to give an example.

As used herein the term ‘impedance parameter’ in reference to someembodiments may refer to impedance or may refer for some embodiments toan electronic parameter such as capacitance or resistance on whichimpedance depends.

In various embodiments “transfer function” may be transfer functionsmapping one input to one output, one input to many outputs, many inputsto many outputs or any collocation or combination of these. To give aspecific example a transfer function may be defined for a singlebiopotential signal to first and second outputs. To give anotherspecific example a transfer function may be defined for first input to afirst output and a second input to a second output.

As used herein “electrode impedance” or “sensor impedance”, are intendedto refer broadly to an impedance between the signal of interest and thesensor or electrode and includes, for example, the impedance formed by acapacitance formed between a surface and a given electrode separated bya layer of dielectric material and/or an air gap.

In various embodiments “circuitry” refers broadly to various suitableelectronics with structure as illustrated or to perform functions asillustrated and these may include analogue circuits, digital circuits,microcontrollers, programmable logic arrays, processors, integratedcircuits, Field Programable Gate Arrays or Application SpecificIntegrated Circuits and virtual machines and includes configurable orprogramable components with suitable configuration or programming code.

In various embodiments the term “processor” refers broadly to any systemor device operable to provide the functionality illustrated or preformsteps or processes illustrated and include analogue circuits, digitalcircuits, microcontrollers, programmable logic arrays, processors,integrated circuits, Field Programable Gate Arrays or ApplicationSpecific Integrated Circuits and virtual machines and includesconfigurable or programable components with suitable configuration orprogramming code.

In various embodiments a signal is ‘captured’ by being ‘reconstructed’from a received signal, parameter values and expressions.

Various embodiments of the invention are implemented as machine readablecode and/or data stored using machine readable media and operable whenread to configure a machine to provide structures illustrated or toperform steps or processes illustrated. In various embodiments themachine-readable media may include semi-permanent media, any computer orprocessor accessible storage, volatile and non-volatile memory.

In various embodiments a sensor has a third electrode. In variousembodiments the third electrode is arranged to have a sensor impedancedefined by a relation dependent on the impedance of one or both of thefirst and second electrodes. For example, the following expression forV_(in) may be referred to as dependent on the variables appearing in theexpression and/or in expressions making up part of the expression forV_(in).

$V_{in} = {\frac{{i_{u1}V_{2}{Z_{2}( {Z_{1} + Z_{f1}} )}} - {H_{12}i_{u2}V_{1}{Z_{1}( {Z_{2} + Z_{f2}} )}}}{( {i_{u1} - {H_{12}i_{u2}}} )( {Z_{1} + Z_{f1}} )( {Z_{2} + Z_{f2}} )}.}$

In various embodiments relations are implemented as equations, vectorequations, vector relations, matrix relations, and data and/or codeand/or tables and/or schema implementing these and any of these may bereferred to as a relation or set of relation in given illustrations ofthe various embodiments.

In various embodiments an unknown impedance parameter may be an unknownelectronic parameter such as capacitance, resistance or inductance onwhich impedance depends. In various embodiments an unknown impedanceparameter may be a real or imaginary component of an electronicparameter such as capacitance, resistance or inductance on whichimpedance depends.

In various embodiments an unknown impedance parameter may be animpedance, resistance or reactance. In various embodiments an unknownimpedance parameter may be a real or imaginary component of impedance,resistance or reactance.

In some embodiments a sensor receiver may be formed of one or moresensor electrodes and a one or more terminals to connect a signalreceived at an electrode to sensing circuitry. In some embodiments asensor receiver may be formed additionally of a means, such as anadhesive layer or strap, to locate the electrode in relation to asurface of a body. In some embodiments a sensor receiver may be formedadditionally of dielectric material located in use between one or moreof the electrodes and a surface of a body.

The reader will appreciate that the receiving the biopotential signal atvarious points or outputs in apparatus such as sensors and circuits isnot limited to the ‘biopotential signal’ being unaffected by theapparatus.

For example a biopotential signal may be received by a sensor electrode,received by a receiver circuit and received at an output of the receivercircuit before being reconstructed by a processor, and the reader willappreciate that reference to ‘biopotential signal’ does not imply thatthe biopotential signal is unaltered between the input of the electrodeand output of the circuit.

In one embodiment the present invention provides a process of capturinga biopotential signal at a surface of a body using a sensor receiverwhich forms a first signal connection with the body wherein one or moreparameters of impedance of the first signal connection are unknown, theprocess comprising:

receiving the biopotential signal at an output of a first signal channelhaving a first channel transfer function which is dependent on the oneor more unknown first impedance parameters;receiving the biopotential signal at an output of a second signalchannel having a second channel transfer function dependent on the oneor more unknown first impedance parameters;solving a set of relations to determine the captured biopotential signalwherein the set of relations is defined dependent on:i) the first channel transfer function,ii) the second channel transfer function, andiv) outputs of the first and second signal channels.

The second channel transfer function may be dependent on the firstunknown impedance parameter by being dependent on a second impedanceparameter which has a known relation to the unknown first impedanceparameter defining a dependence on the unknown first impedanceparameter.

The known relation of the unknown second impedance parameter to theunknown first impedance parameter may be an approximation.

The derived set of relations may comprise a first relation which relatesthe biopotential signal to an expression which is dependent on theoutput signal of the first signal channel, the unknown first impedanceparameter and one or more known parameters for components included inthe first signal channel.

The derived set of relations may comprise a second relation whichrelates the biopotential signal to an expression which is dependent onthe output signal of the second signal channel, an unknown secondimpedance parameter and one or more known parameters for componentsincluded in the second signal channel.

The unknown second impedance and one or more known parameters forcomponents included in the second signal channel may be selected suchthat the second relation does not reduce to the first relation.

The derived set of equations may comprise a third relation which relatesthe unknown second impedance parameter to unknown first impedanceparameter.

The first signal channel may be arranged to have a transfer functionwhich is non-linear with respect to the unknown first impedanceparameter.

The second signal channel may be arranged to have a transfer functionwhich is non-linear with respect to the unknown first impedanceparameter.

The first signal channel may comprise the sensor receiver and afirst-channel circuit having a first known transfer function wherein thefirst channel transfer function is dependent on known componentparameters of the first circuit. The first channel transfer function maybe determined by electronic parameters of the first signal connectionand known electronic parameters of the first circuit. For example, thefirst channel transfer function may be the transfer function of acircuit formed by the sensor receiver connected to the first apparatus,where the component parameters of the first circuit are known. Also, arelation for the biopotential signal may be dependent on the firstchannel transfer function and the output of the first channel whereinthe first channel transfer function may be dependent on known componentparameters of the first channel-circuit and the first unknown impedanceparameter of the first signal connection. The first channel transferfunction may also be dependent on any known component parameters thesensor receiver. To give an illustrative example, the sensor receivermay have a known resistance and may form a capacitive connection withthe body for the biopotential signal of unknown capacitance.

The second signal channel may comprise the sensor receiver and a secondchannel-circuit having a second known transfer function wherein thesecond channel transfer function is dependent on known componentparameters of the second channel circuit. The second channel transferfunction may be determined by electrical parameters of the sensorreceiver and/or the signal connection it forms with the body and also byknown electrical parameters of the second apparatus.

The process may comprise switching a connection from the first sensorreceiver alternately to i) the first-channel circuit to provide a firstchannel transfer function and to ii) the second-channel circuit toprovide a second channel transfer function.

Alternatively, the first sensor receiver may comprise: a first sensorelectrode operable to form a first signal connection to receive thebiopotential signal, wherein the first sensor electrode is connected tothe first-channel circuit to provide the first signal channel andwherein the first sensor receiver; and a second sensor electrodeoperable to form a second signal connection for to receive thebiopotential signal, wherein the second sensor electrode is connected tothe second-channel circuit to provide the second signal channel,

and wherein the second sensor electrode is arranged such that the secondsignal connection has an unknown second impedance parameter which has aknown relation to the unknown first impedance parameter.

The second signal channel may comprise a second sensor receiver whichforms a signal connection with the body having an impedance which is aknown relation with an unknown impedance of the signal connection formedby a first sensor receiver of the first signal channel.

The first sensor receiver may comprise a first sensor electrode whichforms a signal connection with the body for the biopotential signal andthe second sensor receiver may comprise a second sensor electrode whichforms a second signal connection with the body for the biopotentialsignal and the second sensor electrode may be arranged to form a signalconnection with an impedance which has a known relation to the impedanceof the signal connection formed by the first sensor electrode.

The second sensor electrode may have an electrode area arranged to forma signal connection with an impedance which has a known relation to theimpedance of the signal connection formed by the first sensor electrode.

The sensor receiver may have a surface arranged to form a signalconnection formed by the second electrode with an impedance which has aknown relation to the impedance of the signal connection formed by thefirst sensor electrode.

The electrode surface may be arranged to provide a resistance whichforms a signal connection with an impedance which has a known relationto the impedance of the signal connection formed by the first sensorelectrode.

The sensor receiver may comprise one or more conductive layers locatedbetween one or more of the first and second the second electrodes andthe body in use wherein the one or more conductive layers are arrangedso the second sensor receiver forms a signal connection with animpedance which has a known relation to the impedance of the signalconnection formed by the first sensor electrode.

The sensor receiver may comprise one or more dielectric layers locatedbetween one or more of the first and second the second electrodes andthe body in use wherein the one or more dielectric layers are arrangedso the second sensor receiver forms a signal connection with animpedance which has a known relation to the impedance of the signalconnection formed by the first sensor electrode.

The second signal channel may share the unknown impedance parameter withthe first signal channel by the second signal channel sharing with thefirst signal channel an electrode to share the unknown impedanceparameter and the process may switch between first and second signalchannels.

In one embodiment the present invention provides a device operable tocapture a biopotential signal at a surface of a body using a sensorreceiver which forms a first signal connection with the body wherein oneor more parameters of impedance of the first signal connection areunknown, the device comprising:

a first signal channel having a first channel transfer function which isdependent on the one or more unknown first impedance parameters;a second signal channel having a second channel transfer function whichis dependent on the one or more unknown first impedance parameters;a processor operable to solve a set of relations to determine thecaptured biopotential signal wherein the set of relations is defineddependent on:i) the first channel transfer function,ii) the second channel transfer function, andiv) outputs of the first and second signal channels.

The second channel transfer function may be dependent on the firstunknown impedance parameter by being dependent on a second impedanceparameter which has a known relation to the unknown first impedanceparameter.

Embodiments of the present invention provide a sensing device forsensing biopotential signals in a sensing region at a surface of a body,the sensing device comprising:

first and second input terminals for connection to first and secondsensor receivers which each connect the biopotential received at thesurface of the body to a respective receiver terminal, wherein a secondsensor receiver has a second receiver impedance for the biopotentialsignal which has a defined relationship with the receiver impedance ofthe first receiver;sensing circuitry operable to connect to first and second electrodes toreceive first and second electrode signals and to apply a definedtransfer function to the first and second electrode signals to outputfirst and second sensing signals; anda sensing processor operable to determine the biopotential signaldependent on the first and second sensing signals, dependent onparameters of the defined transfer function and dependent on the definedrelationship of the first and second sensor impedances.

The defined transfer function may comprise a first channel transferfunction applied between a first electrode signal and a first outputsignal and a second channel transfer function applied between a secondelectrode signal and a second output signal.

In one embodiment a sensor receiver may comprise one or more capacitiveelectrodes operable to provide a capacitive connection for thebiopotential signal at the surface of the body.

One embodiment may provide a sensor receiver may comprise one or moreconductive electrodes operable to provide a conductive connection forthe biopotential signal at the surface of the body.

The first and second sensor receivers may comprise respective first andsecond electrodes each providing a connection for the biopotentialsignal.

Alternatively, the first and second sensor receivers may have anelectrode common to both receivers. The first and second receivers maycomprise respective first and second sensor rails each connected betweenthe common electrode and a respective first and second receiver terminalto provide a connection for the first and second input terminals of thesensor device.

The sensing processor may be operable to determine the biopotentialsignal using operations defined by a matrix expression for i) transferfunctions of the sensing electronics, ii) the first and second signalvoltages. The expression may be simplified by substitution of impedanceof a second sensor electrode using the known relationship to theimpedance of the first sensor electrode.

Embodiments of the present invention provide a sensor operable to sensea potential signal in a sensing region at a surface of a body with firstand second electrodes which form first and second connections for thepotential signal wherein the impedance of the second connection isdefined relative to the impedance of the first connection. The sensormay provide outputs for the potential signal sensed in the sensingregion via first and second impedances capable of being related by adefined expression.

Embodiments of the present invention provide a sensing electronic deviceoperable to receive a potential signal from a body via first and secondconnections and operable to provide first and second sensing outputswith defined channel transfer functions between each connection and arespective output. The sensing electronic device may be connected toreceive a potential signal via first and second connections having adefined relationship.

Embodiments of the present invention provide signal-determiningelectronics operable to receive first and second sensing signalsprovided by sensing electronics with known parameter values defining afirst and second transfer functions provided by the sensing electronicsfor first and second signals received from first and second electrodesof the sensor and operable to determine a potential signal dependent on:the first and second sensing signals; parameters defining first andsecond transfer functions and dependent on a defined relationship ofimpedances seen by the potential signal at the first and secondelectrodes of the sensor.

Embodiments of the present invention provide a sensing device forsensing a potential signal at a surface of a body wherein the sensingdevice comprises first and second electrodes which each form aconnection for the signal with the body and wherein the connection withthe body formed by the second electrode differs approximately by adefined relationship from the impedance formed by the first electrodewith the body. The relationship may be a factor. The factor may be aninteger.

Embodiments of the invention provide sensing circuitry for sensing apotential signal at a body via a sensor which forms a connection withthe body wherein the sensing electronics comprise a charge amplifierhaving a series impedance capable of connection between a sensor and aninput of an operational amplifier and having a feedback impedance forthe operational amplifier. The series impedance may be arranged todifferentiate the potential signal. The feedback impedance may bearranged to integrate the potential signal.

The sensing circuitry may comprise a first charge amplifier to receiveat a first input an electrode signal from a first sensor electrode whichis operable to form a connection for a biopotential signal and toprovide at a first output a first sensing signal and may comprise asecond charge amplifier operable to receive at a second input a secondelectrode signal from a second electrode which is operable to form aconnection for a biopotential signal and to provide at a second output asecond sensor signal.

The first sensor signal may be the result of a first defined transferfunction applied to the first electrode signal. The first transfersignal may be defined by a feedback impedance of the charge amplifiercircuit and a series impedance in series with an operational amplifierinput. A feedback impedance may be defined by a capacitor and a resistorconnected to define an integrating function for the charge amplifier. Aseries impedance operable to define a differentiation function at theinput of the charge amplifier.

The second sensor signal may be the result of a second defined transferfunction applied to the second electrode signal. The second transfersignal may be defined by a feedback impedance of the charge amplifiercircuit and a series impedance in series with an operational amplifierinput. A feedback impedance may be defined by a capacitor and a resistorconnected to define an integrating function for the charge amplifier. Aseries impedance may be operable to provide a differentiation functionat the input of the charge amplifier.

This allows a determination of the potential signal received via thefirst and second electrodes to be determined dependent on the first andsecond charge amplifier output signals and component values forrespective first and second charge amplifier circuits but independent ofthe impedance of the connection formed by the first electrode and thebody.

The potential signal may be determined independent of the impedanceformed by the first electrode with the body by using an expression forthe biopotential signal derived by equating expressions for thepotential signal dependent on second charge amplifier output signals andcomponent values of respective first and second charge amplifiercircuits and by substituting the impedance formed by the secondelectrode and the body for the product of the sensor factor and theimpedance formed by the first electrode with the body.

This determination may be made by data operations which depend on anexpression for the biopotential signal received at first and secondelectrodes having a known relationship of impedances and dependent onthe first and second sensor signals using wherein the expression isderived from an analytical expression for current at the inputs of theoperational amplifier for a first analytical circuit comprising thefirst charge amplifier and first sensor electrodes connected at thefirst input, an analytical expression for impedance derived fromconservation of current at a node of the operational amplifier of asecond analytical circuit comprising the second charge amplifier andsecond sensor electrode connected at the second input of chargeamplifier circuit and an analytical expression for impedance formed bythe second sensor electrode as a function of the impedance formed by thefirst sensor electrode.

The expression may be derivable using expressions for Kirchhoff's lawsfor current at a node at the input of an operational amplifier. Theexpressions may assume an ideal operational amplifier.

In one embodiment the invention provides a sensor receiver operable toreceive a potential signal in a sensing region at a surface of a bodythe sensor receiver having a first electrode and a second electrode toform first and second sensing connections in the sensing region toreceive the potential signal wherein the electrodes are arranged suchthat the second connection has an impedance which approximately relatesan impedance of the first connection by a defined relation. The definedrelation may be a factor. The defined relation may be a fraction.

The first and/or second electrode may be arranged to form a resistiveconnection with the body for the potential signal.

The first and/or second electrode may be arranged to form a capacitiveconnection with the body for the potential signal.

In another embodiment the invention provides a sensor operable toreceive a potential signal in a sensing region at a surface of a bodythe sensor receiver operable to receive the biopotential signal in thesensing region, wherein the sensor comprises first and second signalpathways to first and second receiver terminals to provide thebiopotential signal received to sensing electronics wherein the secondpathway has an impedance which approximately relates an impedance of thefirst connection by a defined relation.

In another embodiment the invention provides sensor circuitry for apotential signal received at a body by a sensor receiver over an unknownand/or variable impedance, the sensor circuitry comprising first andsecond output channels for first and second output signals each signalcomprising an amplification of the potential signal wherein theamplification is defined by the gain of an operational amplifier with afeedback impedance and with an input impedance

wherein the input impedance is comprised of said unknown and/or variableimpedance and a series impedance between the sensor receiver and theoperational amplifier. The amplification may be negative. Theamplification may be positive. The amplification may be a gain with anabsolute value of greater than one. The amplification may be a gain withan absolute value of one. The amplification may be a gain with anabsolute value of less than one.

The amplification may be provided by operational amplifier circuitshaving feedback and series components.

Alternatively, the amplification may be provided by a transfer functionmodule providing amplification as defined by feedback and seriescomponent values of an operational amplifier.

In another embodiment the invention provides sensor circuitry operableto determine a potential signal received at a body by a one or moreelectrodes forming an unknown and/or variable impedance the sensorcircuitry comprising first and second output channels for first andsecond output signals the transfer function of the potential signal tooutput signals defined by the first and second unknown and/or variablesensor impedances and known component values, wherein the transferfunction to the first and second output signals provide two expressionsfor the unknown potential signal and the unknown sensor impedance. Thiscircuitry allows a sensor which has first and second unknown impedanceswhich have a known relationship to provide a third expression todetermine the two unknown parameters of potential signal and impedance.

In another embodiment the present invention provides a processor fordetermining a potential signal from first and second amplifier signals,each signal comprising an amplified potential signal received by asensor electrode at a body and amplified as defined by an operationalamplifier with defined feedback impedance and defined series impedancesbetween the sensor receiver and the operational amplifier wherein theprocessor is operable to determine a potential signal from the first andsecond amplified signals and, the potential signal determined dependenton an expression for the potential signal which depends on the first andsecond amplified signals,

feedback component values for first and second amplifier circuits andseries impedance values of components at the inputs of the first andsecond operational amplifiers.

The potential signal may be a biopotential signal.

The body may be a body of a biological organism.

A sensing device for sensing a biopotential signal in a sensing regionat a surface of a body the device comprising first and second sensorseach comprising an electrode to provide a connection with the body toreceive the biopotential signal, wherein the second sensor is arrangedto have a connection with the body which has an impedance which isapproximately a factor of an impedance of the first sensor with thebody.

The electrodes of one or more of the first and second sensors may beoperable to form a capacitive connection with the body to receive thebiopotential signal.

The second sensor may be operable to form a capacitance with the bodywhich is approximately a factor of the capacitance formed by the firstelectrode with the body.

The sensing device may comprise a sensing circuit which provides acharge amplifier function for a signal at each sensor, each chargeamplification function defined by a series impedance connected in serieswith the respective sensor and a feedback impedance connected betweenthe series impedance and an output of the circuit.

The sensing circuit may comprise a charge amplifier having one or morefeedback components connected between an output terminal and an inputterminal of an operational amplifier device.

The one or more feedback components feedback components of the chargeamplifier may provide a capacitance and a resistance.

The capacitance provided by the feedback components may be in parallelwith the resistance.

The charge amplifier may comprise one or more series components toprovide a series impedance between the one or more sensor electrodes andthe charge amplifier.

The feedback components may be selected such that for a given seriesimpedance the charge amplifier device provides a gain for a signal intothe series impedance which provides a signal-to-noise ratio for thesignal into the series impedance compared to electromagnetic backgroundnoise which is greater than 0 dB.

The feedback components may be selected such that for a given seriesimpedance and an assumed impedance formed by a sensor electrode and thebody the charge amplifier device provides a gain for the biopotentialsignal which provides a signal-to-noise ratio for the biopotentialsignal compared to electromagnetic background noise which is greaterthan 0 dB.

The feedback components may be selected such that for a given seriesimpedance and an assumed impedance formed by a sensor electrode and thebody the charge amplifier device has an upper frequency of a pass bandwhich is above a frequency range of the biopotential signal which thesensing device is operable to sense.

The feedback components may be selected such that the charge amplifierdevice has a lower frequency of a pass band which is below a frequencyrange of the biopotential signal which the sensing device is operable tosense.

The feedback components and series components may be selected such thatfor an assumed impedance formed by a sensor electrode and the body thecharge amplifier device has an upper corner frequency of a pass bandwhich is above an upper frequency of the biopotential signal which thesensing device is operable to sense.

The feedback components and series components may be selected such thatthe charge amplifier device has a lower corner frequency of a pass bandwhich is below the frequency range of the biopotential signal which thesensing device is operable to sense.

The feedback components may be selected such that the biopotentialsignal of a given frequency range is integrated by the charge amplifyingdevice.

The feedback components and/or the series components may be selected soas to provide a series resistance (R_(s)), feedback resistance (R_(f))and feedback capacitance C_(f) selected such thatR_(f)×C_(f)>R_(s)×C_(f).

The components may be selected such that ratio of unknown capacitancesdefined by the relation does not equal the ratio of series capacitancesat the inputs to the sensing circuitry.

The series components may be selected such that the biopotential signalof a given frequency range is differentiated.

The series components may provide a series capacitance of approximately22 picofarads or more.

The series components may provide a series capacitance of approximately500 picofarads or less.

The series components may provide a series capacitance of approximately100 picofarads or more.

The series components may be selected such that the impedance of theseries components is greater than the impedance formed by the sensor andthe body alone.

The charge amplifier device may provide an output signal for each sensorelectrode.

The sensing device may be operable to sense a biopotential signal withfrequencies above approximately 0.1 Hz.

The sensing device may be operable to sense a biopotential signal withfrequencies approximately 0.5 Hz and above.

The sensing device may be operable to sense a biopotential signal withfrequencies below approximately 1 kHz.

The sensing device may be operable to sense a biopotential signal withfrequencies approximately 150 Hz and below.

The applicant has observed that if the impedance of the second electrodeis equated to the said relationship of impedance of the second electrodethen the impedance of the first sensor can be eliminated from anexpression for the biopotential sensed at both sensors wherein thebiopotential can be determined dependent on the two charge amplifieroutputs, feedback impedances and series impedances.

The sensing device may comprise a processor operable to determine thebiopotential signal dependent on biopotential expression derived fromexpressions for the biopotential sensed via each sensor where theimpedance of the second sensor with the body is substituted for theproduct of the impedance of the first sensor and said impedance factorwherein the bipotential sensed at the second sensor is treated as thebiopotential at the first sensor.

The expression used to determine the biopotential signal from chargeamplifier outputs may be independent of the impedance at the firstsensor wherein the biopotential signal can be determined with an unknownimpedance of the first sensor.

The sensor may have one or more electrodes dimensioned such that aconnection of the second sensor with the body for the biopotentialsignal has an impedance which is approximately a factor of the impedanceof the first electrode with the body.

The capacitive sensor may have two or more electrodes arranged toprovide first and second capacitive signal connections which each havean impedance which differ from each other by a defined relationship. Insome embodiments it the capacitive link that is arranged to differ forthe two electrodes by the defined relationship. This may be as opposedto resistance, for example, in the electrode itself. This may also be asopposed as opposed to a parasitic capacitance of the electrode or acapacitance or resistance which is connected in parallel with theelectrode. In these embodiments the impedance of each capacitive signalconnection provided by a respective electrode may be referred to as afirst or second sensor impedance. For example, a sensor impedance may bedefined predominantly by the capacitance formed between an electrode andskin of the body separated by air or other dielectric material. Thesensor impedances may also be referred to as first and secondsignal-connection impedances. For example, an impedance of a capacitanceformed between a second electrode and skin of a body may be a factor,fraction or defined relationship of an impedance of a capacitance formedbetween a first electrode and skin of the body.

The capacitive sensor may have one or more dielectric layers which,relative one or more dielectric elements of the first capacitive sensor,provide a capacitive connection of the second sensor with the body whichhas an impedance which is approximately a factor of the impedance of thefirst capacitive sensor with the body.

One or more electrodes of the second capacitive sensor may be arrangedco-axial with the one or more electrodes of the electrode of the firstcapacitive element.

One or more electrodes of the second capacitive sensor may be arrangedto have an area which has a defined relationship to the area of one ormore electrodes of the first capacitive element.

One or more electrodes of the second capacitive sensor may be arrangedto have a dielectric layer over the electrode which has a permittivitywhich has a defined relationship to the permittivity of a dielectriclayer over one or more electrodes of the first capacitive element.

The defined relationship in permittivity may be arranged by thickness ofdielectric material.

The defined relationship in permittivity may be arranged by type ofdielectric material.

A sensor may be operable to provide an electrically conductiveconnection with a surface of the body to receive the biopotentialsignal. The sensor may comprise a sensor receiver which has a firstelectrode and a second electrode wherein the second electrode isoperable to provide a connection having an impedance which has a definedrelationship with a connection provided by the first electrode. Thedefined relationship of impedances may be arranged by second and/orfirst electrodes which form differential contact with the surface of thebody.

A sensing device for sensing a biopotential signal in a sensing regionat a surface of a body the device comprising first and second capacitivesensors each comprising a capacitive electrode to provide a capacitiveconnection with the body, wherein the second capacitive sensor isarranged to have a capacitive connection with the body with acapacitance which is approximately a factor of a capacitance of thefirst capacitive sensor with the body.

The capacitive sensor may have one or more electrode dimensions which,relative to dimensions of the electrode of the first capacitive sensor,provide a capacitive signal connection of the second sensor with thebody which has a capacitance with the body which is approximately afactor of the capacitance of the first capacitive sensor with the body.

The capacitive sensor may have one or more dielectric layers which,relative one or more dielectric elements of the first capacitive sensor,provide a capacitive connection of the second sensor with the body whichhas a capacitance with the body which is approximately a factor of thecapacitance of the first capacitive sensor with the body.

One or more electrodes of the second capacitive sensor may be arrangedco-axial with the one or more electrodes of the electrode of the firstcapacitive element.

One or more electrodes of the second capacitive sensor may beinterleaved with the one or more electrodes of the electrode of thefirst capacitive element.

Embodiments of the invention provide a process for reconstructing abiopotential signal from first and second sensing signals output bysensing circuitry which receives first and second electrode signals fromfirst and second sensor electrodes which each form a connection for thebiopotential signal, the process comprising the steps of:

reading first and second sensor signals;reading data carrying information which defines an expression for thebiopotential signal, the expression derived fromi) a first channel expression for the first sensor signal dependent onparameter values for the sensing circuitry providing the first sensorsignal, dependent on the impedance formed by the first electrode anddependent on the biopotential signal, andii) a second channel expression for the second sensor signal dependenton parameter values for the sensing circuitry providing the secondsensor signal, dependent on the impedance formed by the second electrodeand dependent on the biopotential signal, andiii) an expression for the impedance formed by the second electrodedependent on the impedance formed by the first electrode,wherein the expression is derived to eliminate the impedance formed bythe first electrode and eliminate the impedance formed by the secondelectrode; anddetermining the bio-potential signal using said expression for thebiopotential signal to reconstruct the biopotential signal independentlyof the first and second impedance.

The expression for the biopotential signal may be the expression belowsolved for the biopotential, Vin:

${\begin{pmatrix}{TF_{1v}} & {{- i_{u1}}TF_{1v}} \\{TF_{2v}} & {{- H_{12}}i_{u2}TF_{2v}}\end{pmatrix} \cdot \begin{pmatrix}V_{in} \\Z_{u1}\end{pmatrix}} = \begin{pmatrix}V_{1} & {{- i_{u1}}TF_{1i}} \\V_{2} & {{- i_{u2}}TF_{2i}}\end{pmatrix}$

where TF_(1v) is the transfer function between the first sensorelectrode voltage and the first sensing signal output, TF_(1i) is thetransfer function between the first sensor input current and firstsensing signal output, TF_(2v) is the transfer function between thesecond sensor electrode and the second sensing signal, TF_(2i) is thetransfer function between the second sensor input current and secondsensing signal output, i_(u1) is the current through the first sensorelectrode, i_(u2) is the current through the second sensor electrode,Z_(u1) is the unknown impedance formed by the first sensor electrodeand the body, V_(in) is the biopotential signal, V₁ is the first sensorsignal, V₂ is the second sensor signal and H₁₂ is a relationship betweenthe first unknown impedance and the second unknown impedance Z_(u2) suchthat

Z_(u2) = H₁₂Z_(u1)

It is to be understood that the present invention is not limited to theembodiments described herein and further and additional embodimentswithin the spirit and scope of the invention will be apparent to theskilled reader from the examples illustrated with reference to thedrawings. In particular, the invention may reside in any combination offeatures described herein, or may reside in alternative embodiments orcombinations of these features with known equivalents to given features.Modifications and variations of the example embodiments of the inventiondiscussed above will be apparent to those skilled in the art and may bemade without departure of the scope of the invention as defined in theappended claims.

1. An apparatus operable to reconstruct a biopotential signal from asignal received at a surface of a body, the apparatus comprising: asensor device which forms a first signal connection for the biopotentialsignal, the first signal connection having a first sensor impedance, andwhich forms a second signal connection for the biopotential signal, thesecond signal connection having a second sensor impedance, wherein thesensor device is arranged such that the second sensor impedance islinearly related to the first sensor impedance by an impedance relation;sensor circuitry which provides i) a first sensor signal related to thebiopotential signal by a first channel expression which is dependent onparameter values for the sensing circuitry providing the first sensorsignal, dependent on the first sensor impedance and dependent on thebiopotential signal, and ii) a second sensor signal related to thebiopotential signal by a second channel expression which is dependent onparameter values for the sensing circuitry, dependent on the secondsensor impedance and dependent on the biopotential signal; a processoroperable to read data carrying information on parameter values of thereceiver circuitry, operable to read data carrying information on thefirst sensor signal, operable to read data carrying information on thesecond sensor signal and operable to generate data carrying informationon a reconstruction of the biopotential signal said reconstruction usinga derived biopotential relation which is derived from a set of relationscomprising the first channel expression, the second channel expressionand the impedance relation, wherein the derived biopotential relationused to reconstruct the biopotential signal is independent of the firstsensor impedance.
 2. The apparatus of claim 1 wherein a channelexpression defines a transfer function. 3.-48. (canceled)
 49. Theapparatus of claim 2 wherein the transfer function of the first channelcomprises an analytic relation for the gain of a first channelcomprising at least one of a relation to the current entering the firstchannel and a relation to the voltage signal at the entry of the firstchannel, and wherein the transfer function of the second channelcomprises an analytic relation for the gain of a second channelcomprising at least one of a relation for the current entering thesecond channel and a relation to the signal at the entry of the secondchannel.
 50. The apparatus of claim 1, wherein the sensor circuitryprovides a first channel and the first channel expression is:V₁ = i_(u1)TF_(1i) + V_(in)TF_(1ν) + i_(u1)Z_(u1)TF_(1ν) where i_(u1) isthe current entering the channel, V_(in) is the signal at the entry ofthe first channel, V₁ is the output of the first signal channel, Z_(u1)is the first sensor impedance, TF_(1i) is the relation for the gain forthe current entering the first channel, TF_(1v) is a relation for thegain for the signal at the entry of the first channel, and wherein thesensor circuitry provides a second channel and the second channelexpression is: V₂ = i_(u2)TF_(2i) + V_(in)TF_(2ν) + i_(u2)Z_(u2)TF_(2ν)where i_(u2) is the current entering the channel, V_(in) is the signalat the entry of the channel, V₂ is the output of the second signalchannel, Z_(u2) is the unknown second impedance, TF_(2i) is the relationfor the gain to the current entering the second channel, TF_(2v) is therelation for the gain for the signal at the entry of the channel. 51.The apparatus of claim 50 wherein the first signal channel comprises thefirst signal connection in series with sensor circuitry which isarranged so that the first channel transfer function is non-linearlyrelated to the first sensor impedance.
 52. The apparatus of 1 whereinthe impedance relation is: Z_(u2) = H₁₂Z_(u1) + k₁₂ where Z_(u2) is thesecond sensor impedance Z_(u2) is the first sensor impedance, H₁₂ is afactor and k₁₂ is a constant.
 53. The apparatus of claim 52, wherein thederived biopotential relation used by the processor is:$V_{in} = \frac{\begin{matrix}{{H_{12}{i_{u2}( {{- V_{1}} + {i_{u1}TF_{1i}}} )}TF_{2v}} + {i_{u1}TF_{1v}}} \\( {V_{2} - {i_{u2}TF_{2i}} - {i_{u2}k_{12}TF_{2v}}} )\end{matrix}}{( {i_{u1} - {H_{12}i_{u2}}} )TF_{1v}TF_{2v}}$where i_(u1) is a current entering the first channel and i_(u2) enteringthe second channel, i_(u1) is the current entering the channel, V_(in)is the signal at the entry of the first channel, V₁ is the output of thefirst signal channel, Z_(u1) is the first sensor impedance, TF_(1i) isthe relation for the gain for the current entering the first channel,TF_(1v) is a relation for the gain for the signal at the entry of thefirst channel, where i_(u2) is the current entering the channel, V_(in)is the signal at the entry of the channel, V₂ is the output of thesecond signal channel, Z_(u2) is the unknown second impedance, TF_(2i)is the relation for the gain to the current entering the second channel,TF_(2v) is the relation for the gain for the signal at the entry of thechannel, and where Z_(u2) is the second sensor impedance Z_(u2) is thefirst sensor impedance, H₁₂ is a factor and k₁₂ is a constant.
 54. Theapparatus of claim 1 wherein the processor is operable to generate datacarrying information on an estimate of the unknown first impedance usingthe relation:$Z_{u1} = \frac{{( {V_{1} - {i_{u1}TF_{1i}}} )TF_{2v}} + {T{F_{1v}( {{- V_{2}} + {i_{u2}TF_{2i}} + {i_{u2}k_{12}TF_{2v}}} )}}}{( {i_{u1} - {H_{12}i_{u2}}} )TF_{1v}TF_{2v}}$where i_(u1) is a current entering the first channel and i_(u2) enteringthe second channel, i_(u1) is the current entering the channel, V_(in)is the signal at the entry of the first channel, V₁ is the output of thefirst signal channel, Z_(u1) is the first sensor impedance, TF_(1i) isthe relation for the gain for the current entering the first channel,TF_(1v) is a relation for the gain for the signal at the entry of thefirst channel, where i_(u2) is the current entering the channel, V_(in)is the signal at the entry of the channel, V₂ is the output of thesecond signal channel, Z_(u2) is the unknown second impedance, TF_(2i)is the relation for the gain to the current entering the second channel,TF_(2v) is the relation for the gain for the signal at the entry of thechannel, and where Z_(u2) is the second sensor impedance Z_(u2) is thefirst sensor impedance, H₁₂ is a factor and k₁₂ is a constant.
 55. Theapparatus of claim 1 wherein the receiver circuitry is operable tooutput a first current measurement i_(u1) of a current entering thefirst channel and a second current measurement i_(u2) entering thesecond channel.
 56. The apparatus of claim 2 wherein a first channeltransfer function comprises an analytic relation for the gain of a firstchannel comprising an operational amplifier circuit having a selectedfeedback impedance a selected series impedance connected at an input ofan operational amplifier and comprising an impedance in series with theselected series impedance to represent the first sensor impedance, andwherein the second channel transfer function of the second channelcomprises an analytic relation for the gain of a second channelcomprising an operational amplifier circuit having a selected feedbackimpedance a selected series impedance connected at an input of anoperational amplifier and comprising an impedance in series with theselected series impedance to represent the second sensor impedance. 57.The apparatus of claim 2, wherein the transfer function of the firstchannel comprises: $V_{1} = {{- \frac{Z_{f1}}{Z_{s1} + Z_{u1}}}V_{in}}$where V₁ is the output of the first channel, V_(in) is the bipotentialsignal Z_(f1) is a selected first channel feedback impedance, Z_(s1) isa selected first channel series impedance and Z_(u1), is the firstsensor impedance and the transfer function of the second channelcomprises:$V_{2} = {{- \frac{Z_{f2}}{Z_{s2} + {H_{12}Z_{u1}} + k_{12}}}V_{in}}$where V₂ is the output of the second channel, Z_(f2) is a selectedsecond channel feedback impedance, Z_(s2) is a selected second channelseries impedance Z_(u2) is the second sensor impedance, H₁₂ defines arelationship between the first sensor impedance and the second sensorimpedance Z_(u2) such that Z_(u2)=H₁₂ Z_(u1) and wherein thebiopotential signal is reconstructed using the relation$V_{in} = {\frac{V_{1}{V_{2}( {k_{12} + {H_{12}Z_{s1}} - Z_{s2}} )}}{{{- H_{12}}V_{2}Z_{f1}} + {V_{1}Z_{f\; 2}}}.}$58. The apparatus of claim 1 wherein the receiver circuitry comprises afirst receiver circuit having a transfer function defined by a firstfeedback impedance and a first series impedance, wherein the firstreceiver circuit is a charge amplifier, and wherein the charge amplifieris an inverting amplifier with a feedback impedance between an outputand an inverting input and a series impedance at the inverting input.59. The apparatus of claim 1, wherein the biopotential signal, outputsof the receiver circuitry and sensor impedances are defined in thefrequency domain and wherein the processor operates in the frequencydomain.
 60. The apparatus of claim 1, wherein the first channelexpression comprises:$V_{1} = {( {1 + \frac{Z_{f1}}{Z_{1}}} )V_{in}}$ where V₁ isthe output of the first channel, V_(in) is the biopotential signal Z₁ isthe first sensor impedance, Z_(s1) is a selected first channel seriesimpedance and wherein the second channel expression comprises$V_{2} = {( {1 + \frac{Z_{f2}}{Z_{2}}} )V_{in}}$ where V₂ isthe output of the second channel, Z₂ is the second sensor impedance,Z_(f2) is a selected second channel feedback impedance and wherein thebiopotential signal is reconstructed using:$V_{in} = {\frac{V_{2}Z_{2}}{Z_{2} + Z_{f2}}.}$
 61. The apparatus ofclaim 1 wherein, wherein the first channel expression comprises:$V_{1} = {( {1 + \frac{Z_{f1}}{Z_{1}}} )V_{in}}$ where Z₁ thefirst signal impedance signal connection and the transfer function ofthe second channel comprises$V_{2} = {( {1 + \frac{Z_{f2}}{Z_{2}}} )V_{in}}$ where Z₂ isthe second impedance signal and where the derived expression is$V_{in} = \frac{{i_{u1}V_{2}{Z_{2}( {Z_{1} + Z_{f1}} )}} - {H_{12}i_{u2}V_{1}{Z_{1}( {Z_{2} + Z_{f2}} )}}}{( {i_{u1} - {H_{12}i_{u2}}} )( {Z_{1} + Z_{f1}} )( {Z_{2} + Z_{f2}} )}$where i_(u1) is the current entering the first input channel and i_(u2)is the current entering the second input channel.
 62. The apparatus ofclaim 1, wherein the first channel expression comprises:$V_{1} = {\frac{Z_{41}}{Z_{21} + Z_{41}}\frac{( {Z_{11} + Z_{31}} )}{Z_{11}}V_{in}}$where Z₁₁, Z₂₁, Z₃₁ and Z₄₁ are impedance parameters of the first signalchannel, and the second channel expression comprises:$V_{2} = {\frac{Z_{42}}{Z_{22} + Z_{42}}\frac{( {Z_{12} + Z_{32}} )}{Z_{12}}V_{in}}$where Z₁₂, Z₂₂, Z₃₂ and Z₄₂ are impedance parameters of the first signalchannel, and where the captured biopotential signal is determined from:$V_{in} = {\frac{V_{1}V_{2}Z_{11}{Z_{12}( {{Z_{22}Z_{41}} + {( {Z_{41} - {H_{12}( {Z_{21} + Z_{41}} )}} )Z_{42}}} )}}{( {{{- H_{12}}V_{2}{Z_{12}( {Z_{11} + Z_{31}} )}} + {V_{1}{Z_{11}( {Z_{12} + Z_{32}} )}}} )Z_{41}Z_{42}}.}$63. The apparatus of claim 2 wherein the transfer function of each of amultiplicity of n signal channels comprises:V_(n) = i_(un)TF_(ni) + V_(in)TF_(nν) + i_(un)Z_(un)TF_(nν) and whereinthe relation between the unknown first impedance parameter and unknownsecond impedance parameter comprises Z_(un) = H_(1n)Z_(u1) and thecaptured biopotential signal is determined by the processor using$\begin{pmatrix}V_{in} \\Z_{u\; 1}\end{pmatrix} = {\begin{pmatrix}{TF_{1\nu}} & {i_{u1}TF_{1\nu}} \\{TF_{2\nu}} & {H_{12}i_{u2}TF_{2\nu}} \\\vdots & \vdots \\{TF_{n\nu}} & {H_{1n}i_{un}TF_{n\nu}}\end{pmatrix}^{+}\begin{pmatrix}{V_{1} - {i_{u\; 1}{TF}_{1i}}} \\{V_{2} - {i_{u\; 2}{TF}_{2i}} - {i_{u\; 2}k_{12}{TF}_{2v}}} \\\vdots \\{V_{n} - {i_{un}{TF}_{ni}} - {i_{un}k_{1n}{TF}_{nv}}}\end{pmatrix}}$ where A⁺ represents an operator such that if Ax=b, x=A⁺bwhere Z_(u2) is the second sensor impedance Z_(u2) is the first sensorimpedance, H_(1n) is a factor and k₁₂ is a constant, and where TF_(nv) atransfer function.
 64. A process of capturing a biopotential signal at asurface of a body using a sensor receiver which forms a first signalconnection with the body wherein one or more parameters of impedance ofthe first signal connection are unknown, the process comprising:receiving the biopotential signal at an output of a first signal channelhaving a first channel transfer function which is dependent on the oneor more unknown first impedance parameters; receiving the biopotentialsignal at an output of one or more second signal channels each having asecond channel transfer function dependent on the one or more unknownfirst impedance parameters; solving a set of relations to determine thecaptured biopotential signal independently of the unknown one or moreimpedance parameters of the first signal connection, wherein the set ofrelations is defined dependent on: i) the first channel transferfunction, ii) the second channel transfer function, and iii) outputs ofthe first and second signal channels, and wherein the second channeltransfer function is dependent on the first unknown impedance parameterby being dependent on a second impedance parameter which has a knownrelation to the unknown first impedance parameter.
 65. The process ofclaim 64, wherein the solved set of relations comprises a first relationwhich relates the biopotential signal to an expression which isdependent on the output signal of the first signal channel, the unknownfirst impedance parameter and one or more known parameters forcomponents included in the first signal channel.
 66. The apparatus ofclaim 1, wherein the sensor device comprises one or more electrodesoperable to provide a capacitive connection for the biopotential signalat the surface of the body.
 67. The apparatus of claim 1, wherein thesensor device comprises one or more electrodes operable to provide aconductive connection for the biopotential signal at the surface of thebody.
 68. The apparatus of claim 1, wherein the sensor device has anelectrode common to first and second signal connections.
 69. A sensordevice operable to receive a signal from a body, the device arranged toform in use a first signal connection for the biopotential signal, thefirst signal connection having a first sensor impedance, and to form inuse a second signal connection for the biopotential signal, the secondsignal connection having a second sensor impedance, wherein the sensordevice is arranged such that the second sensor impedance is linearlyrelated to the first sensor impedance by a defined impedance relation.